B. suppose 20% of all balls produced by a particular manufacturer are less than 1.680 inches in diameter, and assume that the number of such balls, x, in a sample of two dozen balls can be adequately characterized by a binomial probability distribution. find the mean and standard deviation of the binomial distribution.

Mean = 4.8

Standard deviation = 1.96

Step-by-step explanation:

The mean and standard deviation of the binomial distribution is given by :-

, where n is the total number of trials , p is the the probability of success.

Given : The probability that the produced by a particular manufacturer are less than 1.680 inches in diameter = 20%=0.2

Sample size : n=24                                                 [since 1 dozen = 12]

Now, the  mean and standard deviation of the binomial distribution is given by :-

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