Question

A company sells sunscreen in 450 milliliter (ml) tubes. In fact, the amount of lotion in a tube varies according to a normal distribution with mean μ=448 ml and standard deviation σ=5 ml. Suppose a store which sells this sunscreen advertises a sale for 5 tubes for the price of 4.

Consider the average amount of lotion from a SRS of 5 tubes of sunscreen and find:

(a) The standard deviation of the average, x¯ : equation

(b) The probability that the average amount of sunscreen from 5 tubes will be less than 442 ml.

Answer 1

Solution-a:

standard deviation of the average=S x¯=σ/sqrt(n)=5/sqrt(5)=2.236068

Solution-b:

P(xbar<442)

P(Z<442-448/5/sqrt(5))

P(Z<-6/2.236068)

P(Z<-2.6832)

From standard normal tables

=0.0036

) The probability that the average amount of sunscreen from 5 tubes will be less than 442 ml. is 0.0036