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 ?=498μ=498 ml and standard deviation ?=5σ=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 SRS 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 491 ml. Answer:

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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 ?=498μ=498 ml and standard deviation ?=5σ=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 SRS 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 491 ml.
Answer: 

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