Question

7) In a normal distribution with μ=14 and σ=2, find the mean of the distribution of sample means for samples of size 25.

8) In a normal distribution with μ=12 and σ=0.75, find the standard deviation of the distribution of sample means for samples of size 64. (Round to the nearest ten-thousandth.)

11)Your company manufactures hot water heaters. The life spans of your product are known to be normally distributed with a mean of 13 years and a standard deviation of 1.5 years.

What is the probability that a randomly selected hot water heater has a life span of between 12 and 15 years? (Round to the nearest ten-thousandth.)

Answer 1

_ let X be a random variable bas normal distribution with ll=14 and 0:2 ne 25 i.e. X N N c e, o 2) ... Distribution of sample mean is, X N N (4,02 : Mean of the sample mean is l= 14 Let y be the random variable has normal distribution with =12 and 0 =0.75 given Sample size na 64 ani j.e. Y . NC 4,02) then distribution of sample mean is, N 의 :: Standard deviation of sample mean is eng S.D. o 0.75 0.0937 w let xb is the life spaos of product Die xwNC U=13,0 = (1,5)) 1. P (12<x< 15 )= Pf 12-13 < 3-4 < 15-13) ll, Solis = P(-0.67< < < 1.33) - = 0.65681 -0,67 o 1,33