11.4: Exercises

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1. The physical plant at the main campus of a large state university receives daily requests to replace fluorescent light bulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 56 and a standard deviation of 4. Using the Empirical Rule, what is the approximate percentage of light bulb replacement requests numbering between 56 and 68?

2. A company has a policy of retiring company cars; this policy looks at the number of miles driven, the purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 65 months and a standard deviation of 4 months. Using the Empirical Rule, what is the approximate percentage of cars that remain in service between 57 and 61 months?

3. The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 48 ounces and a standard deviation of 11 ounces. Suggestion: sketch the distribution in order to answer these questions.

a. 99.7% of the widget weights lie between ________ and ________.

b. What percentage of the widget weights lie between 26 and 81 ounces?

c. What percentage of the widget weights lie above 37?

4. For a standard normal distribution, find the following probabilities:

a. $P(z < 1.42)$

b. $P(z > -2.52)$

c. $P(-2.06 < z < 2.81)$

5. For a standard normal distribution, given $P(z < c) = 0.7055$, find $c$.

6. For a standard normal distribution, given $P(z > c) = 0.7109$, find $c$.

7. On a nationwide math test, the mean was 72 and the standard deviation was 10. If Roberto scored 70, what was his z-score?

8. On a nationwide math test, the mean was 66 and the standard deviation was 4. If Roberto scored 75, what was his z-score?

9. On a nationwide math test, the mean was 57 and the standard deviation was 4. If Roberto scored 85, what was his z-score?

10. A quick survey of peanut butter prices had a standard deviation and mean of $0.26 and $3.68, respectively. Compute the area for a peanut butter jar costing less than $3.50.

11. A quick survey of peanut butter prices had a standard deviation and mean of $0.26 and $3.68, respectively. Compute the area for a peanut butter jar costing more than $4.25.

12. A quick survey of peanut butter prices had a standard deviation and mean of $0.26 and $3.68, respectively. Compute the area for a peanut butter jar costing between $3.50 and $4.25.

13. A quick survey of peanut butter prices had a standard deviation and mean of $0.81 and $3.22, respectively. Compute the price for a peanut butter jar costing given the area from the mean is 0.48422.

14. A quick survey of peanut butter prices had a standard deviation and mean of $1.53 and $2.22, respectively. Compute the price for a peanut butter jar costing given the area from the mean is 0.13683.