Chapter 7 Quiz

1. One graph in the figure represents a normal distribution with mean μ=11 and standard deviation σ=3. The other graph represents a normal distribution with mean μ=16 and standard deviation σ=3. Determine which graph is which and explain how you know.

1. Graph A has a mean of 16  and graph B has a mean of 11 because a larger mean shifts the graph to the right.
2. Graph A has a mean of  11 and graph B has a mean of  16 because a larger mean shifts the graph to the left.
3. Graph A has a mean of 16 and graph B has a mean of 11 because a larger mean shifts the graph to the left.
4. Graph A has a mean of 11 and graph B has a mean of  16 because a larger mean shifts the graph to the right.

2. Steel rods are manufactured with a mean length of 28 centimeter​ (cm). Because of variability in the manufacturing​ process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.09 cm. Complete parts ​(a) to ​(d).
​

(a) What proportion of rods has a length less than 27.8 ​cm? ____ (Round to four decimal places as​ needed.)
​(b) Any rods that are shorter than 27.78 cm or longer than 28.22 cm are discarded. What proportion of rods will be​ discarded? ____ ​(Round to four decimal places as​ needed.)
​(c) Using the results of part ​(b)​, if 5000 rods are manufactured in a​ day, how many should the plant manager expect to​ discard? ___ (Use the answer from part b to find this answer. Round to the nearest integer as​ needed.)
​(d) If an order comes in for 10000  steel​ rods, how many rods should the plant manager expect to manufacture if the order states that all rods must be between 27.8 cm and  28.2 ​cm? _____ ​(Round up to the nearest​ integer.)

3.  The mean incubation time of fertilized eggs is 20  days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day.
​(a) Determine the 10th percentile for incubation times.
​(b) Determine the incubation times that make up the middle 39​% of fertilized eggs.

​(a) The 10th percentile for incubation times is ___ days.  ​(Round to the nearest whole number as​ needed.) 
​(b) The incubation times that make up the middle ​39% of fertilized eggs are __ to ___ days.  ​(Round to the nearest whole number as needed. Use ascending​ order.) 

4. The graph of a normal curve is given. Use the graph to identify the value of μ and σ.

5. Assume that the random variable X is normally​ distributed, with mean μ=48 and standard deviation σ=11. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

Which of the following shaded regions corresponds to P(X≤40)​?

6.  The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal​ distribution, with a mean of 15  minutes and a standard deviation of  3 minutes.
​(a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take​ longer, the customer will receive the service for​ half-price. What percent of customers receive the service for​ half-price?
​(b) If the automotive center does not want to give the discount to more than 2 ​% of its​ customers, how long should it make the guaranteed time​ limit?
​(a) The percent of customers that receive the service for​ half-price is ___​%.
​(Round to two decimal places as​ needed.)
​(b) The guaranteed time limit is ___ minutes. ​(Round up to the nearest integer as​ needed.)

Chapter 7 Quiz Answers

1. D. Graph A has a mean of 11 and graph B has a mean of  16 because a larger mean shifts the graph to the right.