Question

A manufacturer of personal computers finds that delivery times for one of their suppliers are random and approximately normally distributed with mean 48.2 minutes and standard deviation 13.4 minutes.

A) What is the probability that a particular delivery will exceed one hour?

B) what is the probability that the mean time of 5 deliveries will exceed one hour?

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	48.2
std deviation   =σ=	13.4000

a)

probability that a particular delivery will exceed one hour:

probability =

P(X>60)

=

P(Z>0.88)=

1-P(Z<0.88)=

1-0.8106=

0.1894

b)

sample size       =n=	5
std error=σx̅=σ/√n=	5.9927

probability =

P(X>60)

=

P(Z>1.97)=

1-P(Z<1.97)=

1-0.9756=

0.0244