Question

Cans of regular coke are labeled as containing 12 oz. Statistics students weighed a sample of 5 randomly selected cans and found the sample mean weight to be 12.02 oz.Assume the cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a population standard deviation if 0.12 oz

a. find the standard error of sampling distribution

b. find the probability that a sample of 5 cans will have a sample mean amount of at least 12.03 oz.

c.find the probability that a sample of 5 cans will have a sample mean between 11.98 oz. and 12.03 oz

Answer 1

Let X be the mean weight of the of 5 cans.

We have sample mean = 12.02, population SD= 0.12 and n=5

From the Central limit theorem,

X~ Normal(12.02, 0.12/√5) distribution

a) Required Standard error= 0.12/√5 = 0.0537

b) We want, P(X>= 12.03)

Using standard normal approximation,

P(z>= 12.03-12.02/0.0537) = P(z>= 0.186) = 0.4262 (from the standard normal distribution tables)

So the required probability is 0.4262

c) P(11.98<X<12.03)

= P(-0.372<z<0.186) = P(z<0.186) - P(z<-0.372) =

P(z<0.186) - P(z>0.372) = 0.5738 - 0.3549= 0.2189

So the required probability is 0.2189