Answer to Question #141004 in Statistics and Probability for ebru

Question

An electronics store has 500 smartphones in stock. Each customer who enters the store can buy as many smartphones as they want, while supplies last. Let Xi be the number of smartphones desired by customer i. Based on their market research, the store knows that the distribution of the number of smartphones desired by a customer has a mean of 0.85 and a standard deviation of 0.6. If 625 customers enter the store today, what is the probability that they will all be able to purchase the smartphones they desire?

Answer 1

E(x)=$\mu=500/625=0.8$

P(x>0.85)=1-P(x<0.85)

P(x<0.85)

z=$(x-\mu)/\sigma$ =(0.85-0.8)/0.6=0.08

using table,for z(0.08), P(x<0.85)=0.53188

P(x>0.85)=1-0.53188=0.4681