Mathematics: 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.

23456789Step-by-step explanation:...

B. suppose 20% of all balls produced by a particular

kitt90335

14.03.2022

Mean = 4.8

Standard deviation = 1.96

Step-by-step explanation:

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

$\mu=np\\\sigma=\sqrt{np(1-p)}$ , 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 :-

$\mu=24\times0.2=4.8\\\\\sigma=\sqrt{24(0.2)(1-0.2)}\\\\=1.95959179423\approx1.96$

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