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In: Statistics and Probability

Applications of the Normal Distribution Read each question carefully and show your work (ie, what you...

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 70^th 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)

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orchestra answered 1 year ago

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