# Normal distributon problems – assume that the mean hourly cost to

1. Assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean of $2,075 per hour and a standard deviation of $225.

What is the operating cost for the lowest 6 percent of the airplanes? (Round z value to 2 decimal places. Omit the “$” sign in your response.)

Operating Costs $

2.The cost per item at a supermarket follows an exponential distribution. There are many inexpensive items and a few relatively expensive ones. The mean cost per item is $6.00. What is the percentage of items that cost:

rev: 10_13_2011

(a) Less than $3.00? (Round your answer to 4 decimal places.)

Probability

3. A uniform distribution is defined over the interval from 6 to 10.

(a) What are the values for a and b?

a

b

________________________________________

(b) What is the mean of this uniform distribution?

Mean

(c) What is the standard deviation? (Round your answer to 2 decimal places.)

Standard deviation

(d) The total area is 1.00.

(e) Find the probability of a value more than 7. (Round your answer to 2 decimal places.)

Probability

(f) Find the probability of a value between 7 and 9. (Round your answer to 1 decimal place.)

Probability

4. The mean of a normal probability distribution is 60; the standard deviation is 5. (Round your answers to 2 decimal places. Omit the % sign in your response.)

(a) About what percent of the observations lie between 55 and 65?

Percentage of observations %

(b) About what percent of the observations lie between 50 and 70?

Percentage of observations %

(c) About what percent of the observations lie between 45 and 75?

Percentage of observations %

7. The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,300 per month and a standard deviation of $220 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed.

What is the probability of selecting a sample of 70 one-bedroom apartments and finding the mean to be at least $2,250 per month? (Round z value to 2 decimal places and final answer to 4 decimal places.)

9 Scrapper Elevator Company has 20 sales representatives who sell their product throughout the United States and Canada. The number of units sold by each representative is listed below. Assume these sales figures to be the population values.

2 3 2 3 3 4 2 4 3 2 2 7 3 4 5 3 3 3 3 5

Compute the Mean of the population (round to 1 decimal place)

10 What is the sign for standard error of the mean?