The diameters of bolts are known to have a standard deviation of 0.0001 inch. A random sample of 10 bolts
yields an average diameter of 0.2546 inch.
i) Test the hypothesis that the true mean diameter of bolts equals 0.255 inch, using α = 0.05.
ii)What size sample would be necessary to detect a true mean bolt diameter of 0.2552 inch or more with a
probability of at least 0.90, assuming α = 0.05?

H0:µ=0.255 at α=0.05.Z=(((OverBar[X])-0.255)/(σ/(Sqrt[n])))

Z=((0.2546-0.255)/(0.0001/(Sqrt[10])))

InverseCDF[NormalDistribution[],1-(0.05/2)]
InverseCDF[NormalDistribution[],(0.05/2)]

we reject H0

d=((μ-(Subscript[μ, 0]))/σ)

d=((0.2552-0.255)/0.0001)

n = 3 is sufficient.