Question

A company sells sunscreen in 450 milliliters (ml) tubes. In fact, the amount of lotion in a tube varies according to a normal distribution with mean ?=446μ=446 ml and standard deviation ?=7σ=7 ml. Suppose a store that sells this sunscreen advertises a sale for 5 tubes for the price of 4. Consider the average amount of lotion from an SRS of 5 tubes of sunscreen and find:

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

(b) The probability that the average amount of sunscreen from 5 tubes will be less than 438 ml.
Answer:  

Answer 1

Solution :

Given that ,

mean = = 446

standard deviation = = 7

n = 5

a)

N ( _, )

= = 446 and

= / n = 7 / 5 = 3.1305

b)

P( < 438) =   P(( - ) / < (438 - 446) / 3.1305)

= P(z < -2.56)   Using standard normal table.   

Probability = 0.0052