Chapter 6.1 Homework

1.   A normal distribution is informally described as a probability distribution that is​ “bell-shaped” when graphed. Draw a rough sketch of a curve having the bell shape that is characteristic of a normal distribution.

Choose the correct answer below.

2.  What does the notation 

indicate? The expression 

denotes the z score with an area of

________

3.   Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

The area of the shaded region is ______  (Round to four decimal places as​ needed.)

4.   Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

The area of the shaded region is ______  (Round to four decimal places as​ needed.)

5.  Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

The area of the shaded region is __________

6.  Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

The indicated z score is  ________  (Round to two decimal places as​ needed.)

7.  Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

The indicated z score is ____________

8.   Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

The indicated z score is _______  (Round to two decimal places as​ needed.)

9.  Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

The indicated z score is _____

10.

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than −0.51 and draw a sketch of the region.

Sketch the region. Choose the correct graph below.

The probability is _______  (Round to four decimal places as​ needed.)

11.  Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than 1.85 and draw a sketch of the region.

Sketch the region. Choose the correct graph below.

The probability is _____  (Round to four decimal places as​ needed.)

12.   Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score greater than 0.45.

Sketch the region. Choose the correct graph below.

The probability is _____

13.   Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score greater than −1.93.

Sketch the region. Choose the correct graph below.

The probability is ______  (Round to four decimal places as​ needed.)

14.   Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. For the case​ below, draw a​ sketch, and find the probability of the reading.​ (The given values are in Celsius​ degrees.)

Between 0.50 and 1.75

Draw a sketch. Choose the correct graph below.

The probability of getting a reading between 0.50°C and 1.75°C is ________  (Round to four decimal places as​ needed.)

15.  Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between −1.55 and −0.94 and draw a sketch of the region.

The probability is _______

16.  Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score between −2.04 and 2.04.

Sketch the region. Choose the correct graph below.

The probability is _______   (Round to four decimal places as​ needed.)

17.   Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is between −2.16 and 3.85 and draw a sketch of the region.

Sketch the region. Choose the correct graph below.

The probability is _______  (Round to four decimal places as​ needed.)

18.  Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than 3.74 and draw a sketch of the region.

Sketch the region. Choose the correct graph below.

The probability is _______  (Round to four decimal places as​ needed.)

19.   Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score greater than 0.

Sketch the region. Choose the correct graph below.

The probability is _______   (Round to four decimal places as​ needed.)

20.   Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score less than 0.

Sketch the region. Choose the correct graph below.

The probability is _____   (Round to four decimal places as​ needed.)