MAT 142 Problem set

Unit: Statistics

Topic: The Normal Distribution

Directions: Solve the following problems. Please show your work, use proper notation and explain your

reasoning.

1. The mean price per ton of grapefruit produced in the United States is $87.76 with a standard

deviation of $23.87. The mean price per ton of grapes used in wine production in the United

States is $125.98 with a standard deviation of $31.44. Assume the price per ton of both

products is normally distributed.

a. A grapefruit producer in Queen Creek, AZ sold his crop for $92.20 per ton. How many

standard deviations above the mean is his price?

b. A vineyard in Ukiah, CA sold his cabernet grapes for $131.52 per ton. How many

standard deviations above the mean was his price?

c. Relatively speaking, who got a better price for his crop? Justify your answer

the person from Queen Creek got a better price for his crop because the z-value is higher.

1. The heart rates for puppies are normally distributed, with a mean heart rate of 180 beats per

minute (60-160 beats per minute for most adult dogs) with a standard deviation of 6 bpm.

a. What percentage of puppies will have heart rates of less than 187 bpm?

b. What percentage of puppies will have heart rates between 175 bpm and 187 bpm?

c. If 500 puppies are examined, how many would you expect to have a heart rate of less

than 187 bpm?

d. 10% of all puppies will have a heart rate greater than what value?