A company sells sunscreen in 400 milliliter (ml) tubes. In fact, the amount of l

Question

A company sells sunscreen in 400 milliliter (ml) tubes. In fact, the amount of lotion in a tube varies according to a normal distribution with mean =396=396 ml and standard deviation =5=5 ml. Suppose a store which sells this sunscreen advertises a sale for 6 tubes for the price of 5. Consider the average amount of lotion from a random sample of 6 tubes of sunscreen and find:

A.The standard deviation of the average, x¯:

B.The probability that the average amount of sunscreen from 6 tubes will be less than 390 ml.

Explanation / Answer

Mean is given as 396 and s is 5. z is defined as (x-mean)/s

a) For a sample of size 6, standard deviation is given as 5/sqrt(6)=2.04

b) P(x<390)=P(z<(390-396)/2.04)=P(z<-2.94) or 1-P(z<2.94)

from normal distribution table we get 1-0.984 or 0.016

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