A company sells sunscreen in 450 milliliter (ml) tubes. In fact, the amount of l

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 =447 ml and standard deviation =5 ml. Suppose a store which sells this sunscreen advertises a sale for 4 tubes for the price of 3. Consider the average amount of lotion from a SRS of 4 tubes of sunscreen and find: (a) The standard deviation of the average, x¯ : (b) The probability that the average amount of sunscreen from 4 tubes will be less than 441 ml. Answer:

Explanation / Answer

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

By central limit theorem,

sigma(X) = sigma/sqrt(n) = 5/sqrt(4) = 2.5 [ANSWER]

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(b) The probability that the average amount of sunscreen from 4 tubes will be less than 441 ml.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    441      
u = mean =    447      
          
s = standard deviation =    2.5      
          
Thus,          
          
z = (x - u) / s =    -2.4      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -2.4   ) =    0.008197536 [ANSWER]

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