Question

Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.3 and a mean diameter of 208

inches.

If 60

shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1

inches? Round your answer to four decimal places.

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	208
std deviation   =σ=	1.300
sample size       =n=	60
std error=σx̅=σ/√n=	0.16783

probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 :

probability =1-P(207.9<X<208.1)=1-P((207.9-208)/0.168)<Z<(208.1-208)/0.168)=1-P(-0.6<Z<0.6)=1-(0.7257-0.2743)=0.5486