1-The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 38 and a standard deviation of 8. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 38 and 62?

2-A company has a policy of retiring company cars; this policy looks at number of miles driven, 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 43 months and a standard deviation of 5 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 28 and 33 months?

3-The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 63 ounces and a standard deviation of 10 ounces.

Use the Standard Deviation Rule, also known as the Empirical Rule.

Suggestion: sketch the distribution in order to answer these questions.

a) 68% of the widget weights lie between?

b) What percentage of the widget weights lie between 33 and 73 ounces?

c) What percentage of the widget weights lie above 43 ?

5-A set of data items is normally distributed with a mean of 113 and a standard deviation of 15. Convert each of the following data items to a z-score. Round your answer to the nearest hundredth.

(a) 118

z =

(b) 55

z =

6-A set of data items is normally distributed with a mean of 29 and a standard deviation of 5.8. Find the data value in the distribution that corresponds to each of the following z-scores. Round your answers to the nearest tenth.

(a) z = -1

(b) z = 0.5

7- Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 243 feet and a standard deviation of 55 feet.

Use your graphing calculator to answer the following questions. Write your answers inpercentform. Round your answers to the nearest tenth of a percent.

a) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 192 feet?P

P

1. (fewer than 192 feet) =%

b) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled more than 204 feet?P

P

1. (more than 204 feet) =

8-The weights of a certain dog breed are approximately normally distributed with a mean of 51 pounds, and a standard deviation of 6.1 pounds. Answer the following questions. Write your answers inpercentform. Round your answers to the nearest tenth of a percent.

a) Find the percentage of dogs of this breed that weigh less than 51 pounds.%

b) Find the percentage of dogs of this breed that weigh less than 46 pounds.%

c) Find the percentage of dogs of this breed that weigh more than 46 pounds.%

9-A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.4 years, and standard deviation of 1.1 years.

The 6% of items with the shortest lifespan will last less than how many years?

Give your answer to one decimal place.

10-Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher's hand. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown below, from which we can see that the speeds of these fastballs follow a Normal model with mean = 92.12 mph and a standard deviation of = 2.43 mph.

Compute thez-score of pitch with speed 87.1 mph. (Round your answer to two decimal places.)

Approximately what fraction of these four-seam fastballs would you expect to have speeds between 91.9 mph and 95.1 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.)

Approximately what fraction of these four-seam fastballs would you expect to have speeds above 95.1 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.)

A baseball fan wishes to identify the four-seam fastballs among the slowest 3% of all such pitches. Below what speed must a four-seam fastball be in order to be included in the slowest 3%? (Round your answer to the nearest 0.1 mph.)