Question

Lisa Mendes and Brad Lee work in the sales department of an AT&T Wireless store. Lisa has been signing up an average of 48 new cell phone customers every month with a standard deviation of 22, while Brad signs up an average of 56 new customers with a standard deviation of 17. The store manager offers both Lisa and Brad 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.

Since neither Lisa or Brad have a very high chance of winning, what would you set as a quota of new customers if you wanted each of them to have at least a 25% chance of winning? Be sure to explain how you calculated your quota.

Answer 1

Q.1.

a) Let, the variable X denotes the spending for men on St.Patrick's Day.

X follow normal ditribution with mean ($\mu$) = $43.87 and standard deviation ($\sigma$) = $3.

We have to find probability that men spend over $50 on St.Patrick's Day.

That is, P(X > 50) = $P(\frac{x-\mu }{\sigma } > \frac{50 - 43.87}{3})$

= P(Z > 2.04)

= 1 - P(Z < 2.04)

= 1 - 0.9793

= 0.0207

b) Let, the variable Y denotes the spending for women on St.Patrick's Day.

Y follows normal ditribution with mean ($\mu$) = $29.54 and standard deviation ($\sigma$) = $11.

We have to find probability that women spend over $50 on St.Patrick's Day.

That is, P(Y > 50) = $P(\frac{Y-\mu }{\sigma } > \frac{50 - 29.54}{11})$

= P(Z > 1.86)

= 1 - P(Z < 1.86)

= 1 - 0.9686

= 0.0314

c) Women are more likely to spend over $50 on St. Patrick's Day.