Question

Liz Mendes and Brad Lee work in the sales department of AT&T Wireless store. Lisa has been signing up an average of 43 new phone customers every month with a Standard deviation of 30, while Brad signs up an average of 52 new customers with a standard deviation d of 25. The store manager offers both a $ 100 incentive bonus if they can sign up more than 100 new customers in a month. assume a normal distribution to answer the following questions.

What is the probability that Lisa will earn $100 incentive bonus?

Answer 1

What is the probability that Lisa will earn $100 incentive bonus?

manager offers $ 100 incentive bonus if they can sign up more than 100 new customers in a month.

Lisa has been signing up an average of 43 new phone customers every month with a Standard deviation of 30

X follows normal distribution with mean 43 and Standard deviation of 30

We need to find P[ X > 100 ]

P[ X > 100 ] = P[ ( X - E(X))/sd(X) > ( 100 - E(X))/sd(X) ]

P[ X > 100 ] = P[ ( X - 43 )/30 > ( 100 - 43 )/30 ]

P[ X > 100 ] = P[ Z > 1.9 ]

P[ X > 100 ] = 1 - P[ Z < 1.9 ]

P[ X > 100 ] = 1 - 0.9713 ( from table )

P[ X > 100 ] = 0.0287

the probability that Lisa will earn $100 incentive bonus is 0.0287