# Math

posted by
**Kay** on
.

8) A consumer groups tries to determine the most expensive items in a convenience store. Four items are

purchased in the convenience store and compared to the average price in stores in the area. Assume tat the

price distribution is normal. Use your calculator to determine the z-score for each.

Item 2 liter Pepsi 12 oz potato chips Load of bread Pizza

Item price - x 2.19 3.79 1.89 13.99

Item mean price -

!

x 1.69 3.29 1.49 11.58

Stand. Deviation price. - s .22 .19 .13 1.17

z-score

Most expensive _____ 2nd most expensive _____ 3rd most expensive _____ cheapest ______

9) In the year 2000, there were 125 major new automobile types available. If you look at the miles per gallon

(MPG) for these vehicles, the distributions are roughly normal. The means and standard deviations are

given in the following chart:

Mean Standard Deviation

City MPG 22.37 4.77

Highway MPG 29.09 5.46

a. The Lincoln Continental had a rating of 17 mpg city and 24 mpg highway. Which rating, city or

highway, is higher compared to the other cars? Show work.

b. The Saturn SL had a rating of 39 mpg city and 43 mpg highway. Which rating, city or highway, is

higher compared to the other cars? Show work.c. The Mazda 626 had a city rating of 26 mpg. What highway rating would it have so that the city and

highway ratings were the same compared to other cars?

10) Two neighboring school districts, Newton and Center Valley compare salaries for its teachers. Assume

normality for distribution of both salaries.

Mean Standard Deviation

Harrison $51,033 $8,654

Center Valley $52,176 $9,299

a. Mr. and Mrs. Newton are married. Mr. Newton works at Harrison and makes $57,000 while Mrs.

Newton works at Center Valley and makes $58,250. Who is higher paid within their school district.

Show work.

b. Mr. and Mrs. Sun are married. Mr. Sun works at Harrison and makes $47,000 while Mrs.

Sun works at Center Valley and makes $48,000. Who is higher paid within their school district.

Show work.

11) In a city parking lot, the average age of a car is 4.65 years with a standard deviation of 1.24 years.

Assuming the distribution of cars is normal. If a car is chosen at random, find the percentage of cars that are

a. older than 5 years b. newer than 2 years

c. less than 1 year old d. between 3 and 6 years. Find the car age that represents:

e. the 85th percentile

f. the 99.5 percentile

g. the oldest 2% h. the youngest 10%

12) Suppose the systolic blood pressure of an adult male is normally distributed with a mean of 138 mm of mercury and standard deviation of 10. If an adult male is picked at random, find the percentage of men whose systolic blood pressure will be a. greater than 160 mm b. between 120 and 135 mm c. less than 110 mm d. between 130 and 140 mm.

Find the systolic blood pressure for men that represents:

e. the 99th percentile f. the 99.5th

percentile g. the top 0.01 percent h. the bottom 0.5 percent

13) The shelf life of milk (properly refrigerated) is normally distributed with a an of 9 days and standard

deviation of 2.8 days. If a gallon of milk is randomly selected what percentage of milk

a. will last more than 2 weeks b. will go bad within a week

c. will last between 1 and 2 weeks d. will last between 8 and 10 days

Find the milk shelf length that represents

e. the 90th

percentile f. the 99.9th

percentile

g. the top 3 percent h. the bottom 1 percent