PERCENTILES: PROBLEM 4 (25 points): Suppose CUNY professors have an average life

Question

PERCENTILES:

PROBLEM 4 (25 points):

Suppose CUNY professors have an average life, normally distributed, of 80 years with a population standard deviation of 9 years.

a)What percent of CUNY professors will live more than 86 years?

b) What percent of CUNY professors will not make it past the age of 50?

c) Calculate the 96th percentile.

d) Calculate the 5nd percentile.

e) What proportion of CUNY professors will live between 75 and 85 years?

PROBLEM 5 (20 points)

Suppose the lifetimes of Hoover vacuum cleaners are normally distributed with an average life () of 12 years and a population standard deviation () of 1.4 years.

a) What proportion of Hoover vacuum cleaners will last 14 years or more?

b) What proportion of Hoover vacuum cleaners will last 7 years or less?

c) What proportion of Hoover vacuum cleaners will last between 11 and 13 years?

d) Calculate the 85th percentile.

e) Calculate the 7th percentile.

PROBLEM 6 (10 points)

Scores of high school seniors taking the English Regents examination in New York State are normally distributed with a mean of 70 and a standard deviation of 10. Find the probability that a randomly selected high school senior will have a score between 70 and 80?

PROBLEM 7 (20 points)

The average individual monthly spending in US for paging and messaging services is $10.50. If the standard deviation is $2.5 and the amounts are normally distributed:

What is the probability that a randomly user pays more than $9.00?

What is the probability that a user pays below $10.00?

Compute the 75% percentile.

Explanation / Answer

Problem 4:

a) The percent of CUNY professors will live more than 86 years is 0.2525 = 25.25%

b) The percent of CUNY professors will not make it past the age of 50 is 0.9996 = 99.96%

c) The 96th percentile is 95.76

d) The 5nd percentile is 65.20

e) The Proportion of CUNY professors will live between 75 and 85 years is 0.4215 = 42.15%

Problem 5:

a) The proportion of Hoover vacuum cleaners will last 14 years or more is 0.07656 = 7.65%

b) The proportion of Hoover vacuum cleaners will last 7 years or less is 0.0001775 = 0%

c) The proportion of Hoover vacuum cleaners will last between 11 and 13 years is 0.5249 = 52.49%

d) the 85th percentile is 13.45

e)The 7th percentile is 9.934

Problem 6: the probability that a randomly selected high school senior will have a score between 70 and 80 is 0.3413

Problem 4:

a) The probability that a randomly user pays more than $9.0 is 0.7257

b) The probability that a user pays below $10.00 is

c) The 75% percentile is 12.19

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