Question

A particular fruit's weights are normally distributed, with a mean of 334 grams and a standard deviation of 6 grams.

If you pick 36 fruits at random, then 13% of the time, their mean weight will be greater than how many grams?

Answer 1

for normal distribution z score =(X-μ)/σx
mean μ=	334
standard deviation σ=	6

sample size       =n=	36
standard error=(σ/√n)*√(N-n)/(N-1))=	6

for top 13% or 87th percentile critical value of z=1.13

therefore corresponding value=mean+z*std deviation=335.13 grams