Question

1. a. "On hold" times for callers to a local cable television company are known to be normally distributed with a standard deviation of 1.4 minutes. Find the average caller "on hold" time if the company maintains that no more than 6% of callers wait more than 5.6 minutes. (Give your answer correct to two decimal places.)

b. Of all mortgage foreclosures in the United States, 45% are caused by disability. People who are injured or ill cannot work--they then lose their jobs and thus their incomes. With no income, they cannot make their mortgage payment and the bank forecloses. 11 mortgage foreclosures are audited by a large lending institution. (Give your answers correct to three decimal places.)

(i) Find the probability of P(Five or fewer of the foreclosures are due to disability)

(ii) Find the probability of P(At least three foreclosures are due to a disability)

Answer 1

Given:

On hold" times for callers to a local cable television company are known to be normally distributed with a standard deviation of 1.4 minutes.

Standard deviation = = 1.4

X = 5.6

The average caller "on hold" time if the company maintains that no more than 6% of callers wait more than 5.6 minutes :

Therefore the average caller "on hold" time if the company maintains that no more than 6% of callers wait more than 5.6 minutes is 3.42

b) Probability of success = p = 0.45

Number of sample = n = 11

Let X be the foreclosures are due to a disability.

X ~ Binomial(n=11, p=0.45)

The probability density function of Binomial Distribution is given by

Therefore

a) The probability of P(Five or fewer of the foreclosures are due to disability) is 0.633

b) The probability of P(At least three foreclosures are due to a disability) is 0.935