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 =7=7 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 random sample of 5 tubes of sunscreen and find:

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

(b) The probability that the average amount of sunscreen from 5 tubes will be less than 388 ml.
Answer:  

Explanation / Answer

Mean is 396 and s is 7. z is calculated as (x-mean)/s

a) standard deviation for sample is 7/sqrt(5)=3.13

b) P(xbar<388)=P(z<(388-396)/(7/sqrt(5))=P(z<-2.56) , this is also 1-P(z<2.56)

from normal distribution table we get 1-0.9948=0.0052

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