The lengths of new pencils are normally distributed with mean 11 cm and standard deviation 0.10 cm. Find the probability that a new pencil picked at random has a length that is: a) Less than 11.15 cm [3 marks] b) Greater than 10.85 cm Between 10.9 cm and 11.1 cm II. The mean number of oil tankers at a port city is eight per day. Find the probability that the number of oil tankers on any given day is: a) Exactly 8 b) At most 3 c) More than 3
Answers
Given data: The lengths of new pencils are normally distributed with mean 11 cm and standard deviation 0.10 cm
.a) Find the probability that a new pencil picked at random has a length that is less than 11.15 cm: Formula used: `Z = (X - μ) / σ`Where,Z = Standard score X = Random Variableμ = Meanσ = Standard Deviation Calculating the value of Z, `Z = (X - μ) / σ = (11.15 - 11) / 0.10 = 1.5`
Now, look up the probability corresponding to the value 1.5 from the Z-Table. P(Z < 1.5) = 0.9332 Hence, the probability that a new pencil picked at random has a length that is less than 11.15 cm is `0.9332` approximately.
b) Find the probability that a new pencil picked at random has a length that is greater than 10.85 cm: Calculating the value of Z, `Z = (X - μ) / σ = (10.85 - 11) / 0.10 = -1.5`Now, look up the probability corresponding to the value -1.5 from the Z-Table. P(Z > -1.5) = P(Z < 1.5) = 0.9332Hence, the probability that a new pencil picked at random has a length that is greater than 10.85 cm is `0.9332` approximately.
c) Find the probability that a new pencil picked at random has a length between 10.9 cm and 11.1 cm:
Calculating the value of Z, Z1 = (X1 - μ) / σ = (10.9 - 11) / 0.10 = -1 and Z2 = (X2 - μ) / σ = (11.1 - 11) / 0.10 = 1Hence, the probability that a new pencil picked at random has a length between 10.9 cm and 11.1 cm is P( -1 < Z < 1 ) = P(Z < 1) - P(Z < -1) = 0.8413 - 0.1587 = 0.6826 approximately. II. The mean number of oil tankers at a port city is eight per day.
a) Find the probability that the number of oil tankers on any given day is exactly 8:P(X = 8)Formula used: `P(X = x) = (e^(-μ) * μ^x) / x!`
Where, X = Random Variableμ = Mean x = Value of Random Variable P(X = 8) = (e^(-8) * 8^8) / 8! = 0.106Hence, the probability that the number of oil tankers on any given day is exactly 8 is `0.106` approximately.
b) Find the probability that the number of oil tankers on any given day is at most 3:
Formula used: `P(X ≤ x) = Σ P(X = i) i=0 to where, X = Random Variable(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = (e^(-8) * 8^0) / 0! + (e^(-8) * 8^1) / 1! + (e^(-8) * 8^2) / 2! + (e^(-8) * 8^3) / 3! = 0.0003Hence, the probability that the number of oil tankers on any given day is at most 3 is `0.0003` approximately.c) Find the probability that the number of oil tankers on any given day is more than 3:Formula used: `P(X > x) = 1 - P(X ≤ x)`Where,X = Random VariableP(X > 3) = 1 - P(X ≤ 3) = 1 - ( P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) ) = 1 - (e^(-8) * 8^0) / 0! + (e^(-8) * 8^1) / 1! + (e^(-8) * 8^2) / 2! + (e^(-8) * 8^3) / 3! = 0.9997Hence, the probability that the number of oil tankers on any given day is more than 3 is `0.9997` approximately.
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Related Questions
what is the raw score that corresponds to a z-score of -2.25 in a population with a mean of 30 and a standard deviation of 6?
Answers
The raw score corresponding to a z-score of -2.25 in a population with a mean of 30 and a standard deviation of 6 is 16.5.
The z-score is the number of standard deviations from the mean, so it is a standardized score.
To solve for a raw score corresponding to a given z-score, we can use the formula:
z = (x - μ) / σ
where z is the z-score,
x is the raw score,
μ is the mean,
and σ is the standard deviation.
Rearranging the formula, we can solve for x : x = μ + (z * σ)
Substituting the given values: μ = 30, σ = 6,
and z = -2.25x
= 30 + (-2.25 * 6) x
= 30 - 13.5 x
= 16.5
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Hello!, im a little stuck on this
Answers
Answer:
61 seats.
Step-by-step explanation:
This is an example of an arithmetic sequence.
The formula for this is an = a + (n - 1)d
Where an is the number of seats in the 19th row, a is the number of seats in the first row, n is the 19th row, and d is the common difference.
We can calculate the common difference by finding how many extra seats there are from the first row to the second. 27 - 25 = 2. So, with each additional row, there are two more seats.
a19 = 25 + (19 - 1) * 2
a19 = 25 + 18 * 2
a19 = 25 + 36
a19 = 61
So, there are 61 seats in the 19th row.
Hope this helps!
Answer:
i think 61 i hope im right
Step-by-step explanation:
n is a positive integer
explain why n(n-1) must be an even number
Answers
Answer:
if 'n' is positive and odd then reducing it by one gives you an even; so then you are multiplying and even and an odd which results in an even
if 'n' is positive and even then reducing it by one gives you an odd; so then you are multiplying and even and an odd which results in an even
Step-by-step explanation:
Find the missing length. (the ?)
Answers
The value of the side EC for the given triangle is 28.75 .
What is triangle proportionality theorem?A line parallel to one side of a triangle splits the other two sides of the triangle proportionally if the line also crosses the other two sides.
In the given triangle,
Side AD = 12, BD = 20 and AC = 56,
Also, the side BC is parallel to side DE.
Let the side EC is x,
Then side AE = 56-x
Since, lines BC and DE are parallel
Therefore, by triangle proportionality theorem,
AD/BD = AE/EC
12/20 = 56-x/x
3/5 = 56-x/x
3x = 230 - 5x
8x = 230
x = 230/8
x = 28.75
The required side EC is 28.75.
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Inside an auditorium, 1 out of 5 people wear hats, and 4 out of 5 people do not wear hats. Based on this information, predict how many wear hats if there are 215 people.
Answers
Answer:
43
Step-by-step explanation:
simplfy y2 when y = -9
Answers
The solution to the expression y² is 81 when y = -9
How to simplify the expression at the given valueFrom the question, we have the following parameters that can be used in our computation:
y = -9
Also, from the question, we have
y2
Express the exponents in the above expression properly
So, we have the following representation
y²
Substitute the known values in the above equation, so, we have the following representation
y² = (-9)²
Remove the bracket in the expression
'This gives
y² = 9²
Evaluate the exponent
So, we have the following representation
y² = 81
Hence, the solution is 81
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If three numbers x, y, and z are chosen at random from the interval [0, 27], what is the probability that the three numbers are a solution to the equation x y z = 27?
Answers
The probability that three numbers are the solution of the equation is 1/27.
Total outcome of the number set
The total possible outcome or numbers in the is 27.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27.
total = 27
three numbers whose products is 27xyz = 27
(1)(3)(9) = 27
probability of the numbers whose product is 27 is calculated as follows;
p = possible numbers / total outcome
p = 1/27
Thus, the probability that three numbers are the solution of the equation is 1/27.
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A support wire is attached to the top of an antenna. The support wire connects
to the ground 15 feet from the bottom of the antenna. The support wire and the
ground meet at an angle with measure 70°, as shown.
Antenna
70°
15 ft-
To the nearest foot, what is the height of the antenna?
The antenna is
feet tall.
Answers
Answer:
Step-by-step explanation:
The antenna height is 41.23 feet if the support wire is attached to the top of the antenna.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
A support wire is attached to the top of an antenna. The support wire connects to the ground 15 feet from the bottom of the antenna.
Let x be the height of the antenna.
We can find the length of the antenna using the trigonometric ratios:
As we know, the trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
Applying tan ratio in the right angle triangle:
tan70 = x/15
x =15tan70
x = 41.212 feet ≈ 41.23 feet
Thus, the height of the antenna is 41.23 feet if the support wire is attached to the top of the antenna.
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write an explicit formula for a subscript n, the nth term of the sequence 8, 11, 14,...
please please help
Answers
The required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values.
here,
The Sequences 8, 11, 14,...
first term a = 8
common difference = 11 - 8 = 3
Now,
The explicit formula is given as,
nth terms = a + (n - 1)d
nth term = 8 + (n - 1)3
Thus, the required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.
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Which of the following regression equations best fits the data shown below?
Answers
Answer:
the answer is A
Step-by-step explanation:
sorry if im worng
what is the perimeter of a rhombus whose diagonals measure 42cm and 56cm?
Answers
Answer:
676
Step-by-step explanation:
d1×d2/2
42×56/2
1352/2=676
please check it by doing again
Answer:
1176
Step-by-step explanation:
=a half the product of its diagonals
=1/2(42x56)
=1176
How many wholes are in 19/3?
Answers
Answer:
6 wholes
Step-by-step explanation:
\( \frac{19}{3} = 6 \frac{1}{3} \)
So there are 6 wholes in 19/3.
2
The graph of f(x) = x is transformed to create
the graph of h(x) = f(x). Which of these
describes the transformation?
Answers
Answer:
The equation f(x) = x represents a straight line passing through the origin with slope 1.
The equation h(x) = f(x) means that we are taking the values of f(x) and using them as the values of h(x). In other words, we are transforming the graph of f(x) without changing its shape. This transformation is simply a vertical translation, where we shift the graph of f(x) up or down by a certain amount.
Since f(x) = x passes through the origin, the transformation h(x) = f(x) will not change the x-intercept of the graph. However, it will shift the entire graph up or down, depending on the value of the constant added to f(x).
Therefore, the transformation h(x) = f(x) represents a vertical translation of the graph of f(x), without changing its shape. The amount of the translation depends on the constant added to f(x), which is not specified in the given equation.
Studio fee:$8 per hour
Vase:$10
Answers
Answer:
4.5 hours
Step-by-step explanation:
So, let's write a function p(x) which represents the total cost.
Let's let x represent the amount of hours.
The cost of a piece is a constant 10.
And there is a $8 fee per hour. In other words:
\(p(x)=8x+10\)
We spent a total of $46.
So, substitute in 46 for p(x) and solve for x:
\(46=8x+10\)
Subtract 10 from both sides:
\(36=8x\)
Divide both sides by 8:
\(x=36/8\)
Reduce:
\(x=4.5\)
So, we spent about 4.5 hours.
Underwood Grocery Store had seven bunches of bananas, and each bunch had six bananas. A customer buys four bananas. Complete and solve the number sentence below to find how many bananas the grocery store has left
Answers
A clay specimen, 25 mm thick, has been tested in an oedometer apparatus with two way rainage, and it is observed that 50% of the consolidation settlement occurs in 1 hour. A ayer of the same clay is observed to settle 10 mm in 10 years and after many years to settle (total primary consolidation) by 35 mm. Determine the thickness of the clay layer if it drains only from upper surface
Answers
The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.
The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.
Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.
Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.
To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.
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2. What rule maps Rectangle RUST onto Rectangle R' U'ST? A. (x,y) → (x+ 5.y-3) B. (x,y) → (x+3,7-5) (x,y) → (x - 5y + 3) (x,y) → (x-3y+5) R
Answers
To find the transformation use one point as reference
U=(-2,6)
U'=(3,3)
Find the difference between U' and U
U' - U = 5, -3
write it refering to any point in the form (x,y)
(x+5,y-3)
The floor of a rectangular shed is 12 ft by 14 ft.
What is the area of the floor in square feet?
Answers
Answer:
Step-by-step explanation:
S=a*b=12*14=168feet²
Data set:6 numbers;median=14;mode=1
Answers
Answer:
Yes; what's the whole data set ?
Step-by-step explanation:
what’s the answer to this?
Answers
Answer:9
Step-by-step explanation:because when we add 7+7+6+6=26 then we will going to 35-26= 9 im not sure so don’t hate me if it was wrong
WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER
Answers
Answer:
(3,5)
Step-by-step explanation:
We first need to substitute x for 3 in the equation :)
y = 2(3) - 1
y = 6 - 1
y = 5
The cordinate will be (3,5)
Have an amazing day!!
Please rate and mark brainliest!!
Help.......................
Answers
Answer:
50% will be your answer
Answer:
50%
Step-by-step explanation:
half of 1 whole which is 100% is always 50% or 1/2
Given x varies inversely as y and x = 4 when y=−9, find y when x = 6.
Answers
Given that X varies inversely as Y, the value of Y when the number of X is increased to the given value is -6.
What is Proportional relationships?Proportional relationships are relationships between two variables where their ratios are equivalent.
Inverse variation It is expressed as;
x ∝ 1/r then x = k/y
Where k is the proportionality constant.
Given the data in the question;
x = 4y = -9First we find the proportionality constant.
x = k/y
4 = k / -9
k = -36
Now, If x = 6 then y = ?
x = k/y
6 = -36 / y
6y = -36
y = -36 / 6
y = -6
Given that X varies inversely as Y, the value of Y when the number of X is increased to the given value is -6.
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Find all roots of the polynomial
p(x)= x^4 - 5x^3 + 7x^2 - 5x + 6 ; i
Answers
Answer:
The roots of p(z) are z = i, 2.91367 + 0.600499i, 1.22097 - 0.362212i, 0.306704 + 1.53771i.
Find the original price, discount, sale price, or selling price. Original price: $130 Markup: 35% Selling price: _____
Answers
Step-by-step explanation:
Original price : $130
Discount : 35% × $130
= $45.50
sale price : $130 - $45.50
= $84.50
Stan and Talia each went to see a movie. Both movies started at 7:15.
Stan's movie ended at 9:40.
Talia's movie ended at 10:10.
Part A
Use the drop-down menus to complete the sentence about the length of Stan's movie.
Stan's movie lasted
Choose...
hours and
Choose...
minutes.
Part B
Use the drop-down menus to complete the sentence that compares the length of the two movies.
Talia's movie lasted
Choose...
hours and
Choose...
minutes longer than Stan's movie.
Answers
The length of Stan's movie is 2 hours 25 minutes
The length of Talia's movie is 2 hours 55 minutes.
What are the length of the movies?In order to determine the length of the movies, subtract the end time of the movie from the time the movie started.
Subtraction is the mathematical operation that is used to calculate the difference between two or more numbers. The sign that is used to represent subtraction is -.
Length of the movie = time the movie ended - time the movie started
Length of Stan's movie = 9:40 - 7:15 = 2 : 25 hours
Length of the Talia's movie = 10 : 10 - 7 : 15 = 2 : 55 hours
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Construct a confidence interval for μ assuming that each sample is from a normal population. (a) x
ˉ
=28,σ=4,n=11,90 percentage confidence. (Round your answers to 2 decimal places.) (b) x
ˉ
=124,σ=8,n=29,99 percentage confidence. (Round your answers to 2 decimal places.)
Answers
The confidence interval in both cases has been constructed as:
a) (26.02, 29.98)
b) (120.17, 127.83)
How to find the confidence interval?The formula to calculate the confidence interval is:
CI = xˉ ± z(σ/√n)
where:
xˉ is sample mean
σ is standard deviation
n is sample size
z is z-score at confidence level
a) xˉ = 28
σ = 4
n = 11
90 percentage confidence.
z at 90% CL = 1.645
Thus:
CI = 28 ± 1.645(4/√11)
CI = 28 ± 1.98
CI = (26.02, 29.98)
b) xˉ = 124
σ = 8
n = 29
90 percentage confidence.
z at 99% CL = 2.576
Thus:
CI = 124 ± 2.576(8/√29)
CI = 124 ± 3.83
CI = (120.17, 127.83)
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2x-5y=11,4x+10y=18
Use elimination
Answers
Answer:
Step-by-step explanation:
Reza Nazari, Ava Ross · 2019 · Study Aids
18) Choice D is correct sum of terms sum of numbers average ... –2(2x + 5y = 11) , –4x – 10y = —22 4x – 2y = –14 4x – 2y = –14 = –12y = —36 = y = 3 Plug in ...
AABC is reflected across the x-axis and then dilated by a factor of 2 using the
point (-2, 1) as the center of dilation. What is the transformation of A(3, 1)?
6-
C(2,4)
4
B (5, 3)
2+
A (3.1)
4
-2-
OA. A(-6, 2)
B. A (6, -2)
C. A (8,-3)
D. A(3,-1)
-4
-2
N+
746
+00
8
10
Answers
The transformation of A is A' = (8, -3)
How to determine the transformation?From the graph, we have:
A = (3,1)
The scale factor and the center of dilation are given as:
k = 2
(a,b) = (-2,1)
The rule of reflection across the axis is:
(x,y) ⇒ (x,-y)
So, we have:
A' = (3,-1)
The rule of dilation is represented as:
(x,y) ⇒ (k(x - a) + a, k(y - b) + b)
So, we have:
A' = (2(3 + 2) - 2, 2(-1 - 1) + 1)
Evaluate
A' = (8, -3)
Hence, the transformation of A is A' = (8, -3)
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How's the economy? A pollster wants to construct a 95% confidence interval for the proportion of adults who believe that economic conditions are getting better. Part 1 of 2 (a) A poll taken in July 2010 estimates this proportion to be 0.25. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.02?A sample of 861.3 adults is needed to obtain a 95% confidence interval with a margin of error of 0.02. (b) Estimate the sample size needed if no estimate of p is available. adults is needed to obtain a 95% confidence interval with a margin of error A sample of of 0.02.
Answers
To construct a confidence interval for the proportion of adults who believe that economic conditions are getting better, the pollster needs to consider the sample size and margin of error.
In part (a), the pollster has an estimate of the proportion (0.25) and wants a margin of error of 0.02 with a 95% confidence interval. To determine the sample size needed, the pollster can use the formula:
sample size = (Z^2 * p * q) / E^2
where Z is the z-score for the confidence level (1.96 for 95%), p is the estimated proportion (0.25), q is 1-p, and E is the margin of error (0.02).
Plugging in these values, we get:
sample size = (1.96^2 * 0.25 * 0.75) / 0.02^2
sample size = 861.3
Therefore, a sample size of 862 adults is needed to obtain a 95% confidence interval with a margin of error of 0.02, based on the estimate of 0.25.
In part (b), if no estimate of p is available, the pollster can use a conservative estimate of p = 0.5 to calculate the sample size needed. This is because a sample size calculated using p = 0.5 will be the largest sample size needed for any value of p.
Using the same formula as before, we get:
sample size = (1.96^2 * 0.5 * 0.5) / 0.02^2
sample size = 2401
Therefore, a sample size of 2401 adults is needed to obtain a 95% confidence interval with a margin of error of 0.02, without an estimate of p.
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