Question 1

Use the following to answer the questions below:
Select the answer closest to the specified areas for a N(0, 1) density. Round to three decimal places.
-The area to the left of z = 0.63.
A) 0.736
B) 0.264
C) 0.525
D) 0.041

Accepted Answer

The area to the left of z = 0.63 in a standard normal distribution (N(0, 1)) is approximately 0.736, which can be found using a standard normal distribution table or a calculator.

Question 2

Use the following to answer the questions below:
Select the answer closest to the specified areas for a N(0, 1) density. Round to three decimal places.
-The area to the right of z = -0.47.
A) 0.341
B) 0.770
C) 0.681
D) 0.319

Accepted Answer

The area to the right of z = -0.47 in a standard normal distribution is found by looking up the z-score in a standard normal table or using a calculator. The area to the left of z = -0.47 is approximately 0.319, so the area to the right is 1 - 0.319 = 0.681.

Question 3

Use the following to answer the questions below:
Select the answer closest to the specified areas for a N(0, 1) density. Round to three decimal places.
-The area between z = 0.51 and z = 2.79.
A) 0.695
B) 0.302
C) 0.692
D) 0.997

Accepted Answer

B

Question 4

Use the following to answer the questions below:
Select the answer closest to the specified areas for a N(0, 1) density. Round to three decimal places.
-The area outside of the interval z = -2.13 and z = 1.11.
A) 0.133
B) 0.017
C) 0.850
D) 0.150

Accepted Answer

The area outside the interval z = -2.13 and z = 1.11 is found by calculating 1 minus the area between these z-scores. The cumulative area from z = -2.13 to z = 1.11 is approximately 0.850, so the area outside is 1 - 0.850 = 0.150.

Question 5

Use the following to answer the questions below:
Find the endpoint(s) on a N(0, 1) density with the given property. Round to three decimal places.
-The area to the left of the endpoint is about 0.20.
A) -2.054
B) 0.842
C) -0.842
D) 2.054

Accepted Answer

The area to the left of the endpoint in a standard normal distribution (N(0, 1)) that corresponds to 0.20 is approximately -0.842.

Question 6

Use the following to answer the questions below:
Find the endpoint(s) on a N(0, 1) density with the given property. Round to three decimal places.
-The area to the right of the endpoint is about 0.85.
A) -1.036
B) 1.036
C) -0.842
D) 1.375

Accepted Answer

The answer of Use the following to answer the questions...

Question 7

Use the following to answer the questions below:
Find the endpoint(s) on a N(0, 1) density with the given property. Round to three decimal places.
-The area between ±z is about 0.88.
A) 1.175
B) 1.645
C) 1.275
D) 1.555

Accepted Answer

The answer of Use the following to answer the questions...

Question 8

Use the following to answer the questions below:
Select the answer closest to the specified areas for a normal density. Round to three decimal places.
-The area to the left of 32 on a N(45, 8) distribution.
A) 0.948
B) 0.052
C) 0.896
D) 0.104

Accepted Answer

The answer of Use the following to answer the questions...

Question 9

Use the following to answer the questions below:
Select the answer closest to the specified areas for a normal density. Round to three decimal places.
-The area to the right of 12 on a N(60, 4) distribution.
A) 0.691
B) 0.383
C) 0.617
D) 0.309

Accepted Answer

The answer of Use the following to answer the questions...

Question 10

Use the following to answer the questions below:
Select the answer closest to the specified areas for a normal density. Round to three decimal places.
-The area between 43 and 100 on a N(14, 3) distribution.
A) 0.985
B) 0.122
C) 0.863
D) 0.878

Accepted Answer

The area between 43 and 100 on a N(14, 3) distribution is 0.863.

Question 11

Use the following to answer the questions below:
Find the endpoint(s) on the normal density curve with the given property. Round to three decimal places.
-The area to the left of the endpoint on a N(54, 2.5) curve is about 0.15.
A) 51.409
B) 56.591
C) 59.425
D) 48.575

Accepted Answer

The z-score corresponding to an area of 0.15 to the left is approximately -1.036. Using the formula for converting a z-score to an x-value (x = μ + zσ), where μ = 54 and σ = 2.5, we get x = 54 + (-1.036)(2.5) = 51.409.

Question 12

Use the following to answer the questions below:
Find the endpoint(s) on the normal density curve with the given property. Round to three decimal places.
-The area to the right of the endpoint on a N(26, 4) curve is about 0.4.
A) 18.997
B) 24.987
C) 33.003
D) 27.013

Accepted Answer

The answer of Use the following to answer the questions...

Question 13

Use the following to answer the questions below:
Find the endpoint(s) on the normal density curve with the given property. Round to three decimal places.
-The symmetric middle area on a N(12, 4) curve is about 0.75.
A) 4.160 and 19.840
B) 7.399 and 16.601
C) 9.302 and 14.698
D) 6.874 and 17.126

Accepted Answer

The answer of Use the following to answer the questions...

Question 14

Use the following to answer the questions below:
It is generally believed that the heights of adults males in the U.S. are approximately normally distributed with mean 70 inches (5 feet, 10 inches) and standard deviation 3 inches and that the heights of adult females in the U.S. are also approximately normally distributed with mean 64 inches (5 feet, 4 inches) and standard deviation 2.5 inches. A small university is considering custom ordering beds for their dorm rooms. Answer the following questions about the lengths of beds in dorm rooms at this university.
-Draw a sketch of the distribution of women's heights and label at least three points on the horizontal axis.

Accepted Answer

The answer of Use the following to answer the questions...

Question 15

Use the following to answer the questions below:
It is generally believed that the heights of adults males in the U.S. are approximately normally distributed with mean 70 inches (5 feet, 10 inches) and standard deviation 3 inches and that the heights of adult females in the U.S. are also approximately normally distributed with mean 64 inches (5 feet, 4 inches) and standard deviation 2.5 inches. A small university is considering custom ordering beds for their dorm rooms. Answer the following questions about the lengths of beds in dorm rooms at this university.
-The beds that the university currently purchases are 75 inches long. What proportion of males will be able to fit on the bed while lying perfectly straight? Round your answer to three decimal places.

Accepted Answer

Need to find area on a N(70, 3) distribution to the left of 75.

Question 16

Use the following to answer the questions below:
It is generally believed that the heights of adults males in the U.S. are approximately normally distributed with mean 70 inches (5 feet, 10 inches) and standard deviation 3 inches and that the heights of adult females in the U.S. are also approximately normally distributed with mean 64 inches (5 feet, 4 inches) and standard deviation 2.5 inches. A small university is considering custom ordering beds for their dorm rooms. Answer the following questions about the lengths of beds in dorm rooms at this university.
-Should the university be concerned that females will not fit in the 75 inch beds?

Accepted Answer

The average height of adult females is 64 inches, which is well below the 75-inch bed length, so the university should not be concerned about females not fitting in the beds.

Question 17

Use the following to answer the questions below:
It is generally believed that the heights of adults males in the U.S. are approximately normally distributed with mean 70 inches (5 feet, 10 inches) and standard deviation 3 inches and that the heights of adult females in the U.S. are also approximately normally distributed with mean 64 inches (5 feet, 4 inches) and standard deviation 2.5 inches. A small university is considering custom ordering beds for their dorm rooms. Answer the following questions about the lengths of beds in dorm rooms at this university.
-The university plans on ordering custom sized beds such that 99% of male students are expected to fit in them when lying perfectly straight. What length beds should they order? Round your answer to the nearest inch.
A) 77 inches
B) 78 inches
C) 76 inches
D) 75 inches

Accepted Answer

The endpoint of the N(70, 3) density that has 99% to the left of it is 76.978, or about 77.
If they want 99% of male students to fit in them when lying perfectly straight, they should order the beds to be 77 inches long.

Question 18

Use the following to answer the questions below:
It is generally believed that the heights of adults males in the U.S. are approximately normally distributed with mean 70 inches (5 feet, 10 inches) and standard deviation 3 inches and that the heights of adult females in the U.S. are also approximately normally distributed with mean 64 inches (5 feet, 4 inches) and standard deviation 2.5 inches. A small university is considering custom ordering beds for their dorm rooms. Answer the following questions about the lengths of beds in dorm rooms at this university.
-The university decides it is too expensive to replace all the beds. Suppose the university has 2,150 beds all of which are 75 inches long. How many beds should they replace? You may assume that only those males taller than 75 inches will receive the longer beds and that females make up half of the population that will need a dorm room bed.
A) 52 beds
B) 44 beds
C) 32 beds
D) 28 beds

Accepted Answer

To find the number of males taller than 75 inches, calculate the z-score: (75 - 70) / 3 = 1.67. Using the standard normal distribution table, the proportion of males taller than 75 inches is about 0.0475. With 1,075 males (half of 2,150), the number needing longer beds is 1,075 * 0.0475 ≈ 51.06, rounded to 52 beds.

Question 19

Use the following to answer the questions below:
In the following, convert an area from one normal distribution to an equivalent area for a different normal distribution. Show details of your calculation. Draw sketches of both normal distributions, find and label the endpoints, and shade the regions on both curves.
-The area to the left of 16 for a N(20, 3) distribution converted to a standard normal distribution

Accepted Answer

The answer of Use the following to answer the questions...

Question 20

Use the following to answer the questions below:
In the following, convert an area from one normal distribution to an equivalent area for a different normal distribution. Show details of your calculation. Draw sketches of both normal distributions, find and label the endpoints, and shade the regions on both curves.
-The "Q1" for a standard normal distribution converted to a N(15, 2.5) distribution.

Accepted Answer

The answer of Use the following to answer the questions...

Quiz 5: Approximating With a Distribution

Use the following to answer the questions below: Select the answer closest to the specified areas for a N(0, 1) density. Round to three decimal places. -The area to the left of z = 0.63.

Use the following to answer the questions below: Select the answer closest to the specified areas for a N(0, 1) density. Round to three decimal places. -The area to the right of z = -0.47.

Use the following to answer the questions below: Select the answer closest to the specified areas for a N(0, 1) density. Round to three decimal places. -The area between z = 0.51 and z = 2.79.

Use the following to answer the questions below: Select the answer closest to the specified areas for a N(0, 1) density. Round to three decimal places. -The area outside of the interval z = -2.13 and z = 1.11.

Use the following to answer the questions below: Find the endpoint(s) on a N(0, 1) density with the given property. Round to three decimal places. -The area to the left of the endpoint is about 0.20.

Use the following to answer the questions below: Find the endpoint(s) on a N(0, 1) density with the given property. Round to three decimal places. -The area to the right of the endpoint is about 0.85.

Use the following to answer the questions below: Find the endpoint(s) on a N(0, 1) density with the given property. Round to three decimal places. -The area between ±z is about 0.88.

Use the following to answer the questions below: Select the answer closest to the specified areas for a normal density. Round to three decimal places. -The area to the left of 32 on a N(45, 8) distribution.

Use the following to answer the questions below: Select the answer closest to the specified areas for a normal density. Round to three decimal places. -The area to the right of 12 on a N(60, 4) distribution.

Use the following to answer the questions below: Select the answer closest to the specified areas for a normal density. Round to three decimal places. -The area between 43 and 100 on a N(14, 3) distribution.

Use the following to answer the questions below: Find the endpoint(s) on the normal density curve with the given property. Round to three decimal places. -The area to the left of the endpoint on a N(54, 2.5) curve is about 0.15.

Use the following to answer the questions below: Find the endpoint(s) on the normal density curve with the given property. Round to three decimal places. -The area to the right of the endpoint on a N(26, 4) curve is about 0.4.

Use the following to answer the questions below: Find the endpoint(s) on the normal density curve with the given property. Round to three decimal places. -The symmetric middle area on a N(12, 4) curve is about 0.75.