Question

A local AT&T wireless retail center waits 4 days to receive a shipment of iPhones to replenish inventory (known as the lead-time). Demand during this lead-time period for iPhones follows the normal distribution with a mean of 50 phones and standard deviation of 9 phones.

a. Define the random variable and its probability distribution.

b. What is the probability that, during the next lead-time, demand for iPhones will be less than 42 phones?

c. What is the probability that, during the next lead-time, demand for iPhones will be less than 54 phones?

d. What is the probability that, during the next lead-time, demand for iPhones will be equal to 54 phones?

Answer 1

a)

here random variable X is Demand during the lead-time period for iPhones whcih follows the normal distribution with a mean of 50 phones and standard deviation of 9 phones.

b)

here mean=       μ=	50
std deviation   =σ=	9.000

probability =P(X<42)=(Z<(42-50)/9)=P(Z<-0.89)=0.1867

c)

probability =P(X<54)=(Z<(54-50)/9)=P(Z<0.44)=0.6700

d)

P(X=54) =0 (since probability of a point estimate is 0 on a continuous variable since area under a point overt a curve is 0)