Question

The number of days (X) after mailout it takes a utility company to receive payment for a customer’s bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days. There is a probability of 0.50 that a bill will be received later than days after mailout.

Answer 1

Solution:

We are given that: X : The number of days after  mailout it takes a utility company to receive payment for a customer’s bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days.

That is: .

Properties of Normal Distribution:

i) Normal distribution is symmetric about center, that is about the mean of the distribution.

ii) Normal distribution has bell shaped curve

iii) Since Normal distribution is symmetric about mean, 50% of data fall below mean and rest 50% data fall above mean.

That is there is 0.5 probability that variable takes a value less than mean , similarly there is 0.5 probability that variable takes a value more than mean.

Since Mean = 31, there is 0.50 probability that a bill will be received later than 31 days after mailout.

Thus required answer is: 31