In: Statistics and Probability
Applications of the Normal Distribution
Read each question carefully and show your work (ie, what you put into the calculator)!!
1. Cherry trees in a certain orchard have heights that are normally distributed with a mean of 110 inches and a standard deviation of 13 inches. What is the probability that a randomly selected tree is:
a) More than 115 inches tall?
(round to 4 decimals)
b) Less than 95 inches tall?
(round to 4 decimals)
c) Between 95 and 105 inches tall?
(round to 4 decimals)
2. A survey among freshmen at a certain university revealed that the number of hours spent
studying the week before final exams was normally distributed with a mean of 25 hours and a
standard deviation of 7 hours.
a) Calculate the 70th percentile of the number of hours spent studying.
(Round to the nearest whole number)
b) Find the cutoffs for the middle 70% of the number of hours spent studying.
(Round to the nearest whole number)
3. The Real Estate Group NY reports that the mean monthly rent for a one-bedroom apartment
(without a doorman) in Manhattan is $2630 with a standard deviation of $400.
A real estate firm samples 100 apartments.
a) What is the probability that the mean rent is greater than $2700?
(round to 4 decimals)
b) What is the probability that the mean rent is between $2500 and $2600?
(round to 4 decimals)