Question

A company sells sunscreen in 500 milliliter (ml) tubes. In fact, the amount of lotion in a tube varies according to a normal distribution with mean ?=498 ml and standard deviation ?=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, ?¯ :

(b) The probability that the average amount of sunscreen from 5 tubes will be less than 491 ml. Answer:

Answer 1

Solution :

Given that ,

mean = = 498

standard deviation = = 5

n = 5

= 498

(a) = / n = 5 / 5 = 2.2361

Standard deviation = 2.2361

(b) P( < 491)

= P(( - ) / < (491 - 498) / 2.2361)

= P(z < -3.13)

Using z table

= 0.0009

Answer : Probability = 0.0009