**Introduction to Statistics – MATO 205**

**Quiz 2: Chapter 6**

**Name** ______________________________________________ **Date** _______________

**Fill in the space. (1 points each)**

For a continuous probability distribution, the total area under the curve is equal to _____ .

Which of the following is NOT a characteristic of the normal distribution? (bell-shaped, symmetrical, discrete, asymptotic – pick one) _________________.

How many normal distributions are there? (1, 10, 30, infinite – pick one) __________ .

The signed difference between a selected value and the mean divided by the standard deviation is called a ______________.

What is the probability of a z value between -2.03 and 1.76? _____________.

What is the probability of a value between and 0? ______________.

What is the probability of a value between and ? ____________.

**Circle the best answer for each of the following: (1 points each)**

Ella refuses to tell you her weight in her ninth month of pregnancy. However, she does tell you that her weight is above the mean. Which of the following -scores is possible for her weight?

1.43

Not enough information

Candy was surprised when the doctor told her that her baby’s weight was in the 85th percentile. If baby’s weights are normally distributed, which of the following would be a reasonable standard score for her baby’s weight?

85

04

Not enough information

One of the values in a normal distribution is 43 and its *z*-score is 1.65. If the mean of the distribution is 40, what is the standard deviation?

3 **B.** –1.82 **C.** .55 **D.** 1.82 **E.** -.55

**Free Response Question: You must show your work to earn full credit.**

Find each specified probability.

a. (2 points) |
1. (2 points) |

1. (3 points) |
1. (3 points) |

The accounting department at Weston Materials Inc., a natural manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution.

Determine the z values for 29 and 34 hours. **(15 points)**

What percent of the garages take between 29 hours and 34 hours to erect?

What percent of the garages take between 32 hours and 34 hours to erect?

What percent of the garages take 28.7 hours or less to erect?

Of the garages, 5% take how many hours to erect?

The IRS reports that the mean refund for a particular group of taxpayers was $1,600. The distribution of tax refunds follows a normal distribution with a standard deviation of $850.

**(15 points)**

What percentage of the refunds are between $1,600 and $2,000?

What percentage of the refunds are between $900 and $2,000?

What percentage of the refunds are between $1,800 and $2,000?

What percentage of the refunds are less than $1,000?

Ninety-five percent of the refunds are less than what amount?