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.
Accepted Solution
A:
Answer: Mean = 4.8 Standard deviation = 1.96Step-by-step explanation:The mean and standard deviation of the binomial distribution is given by :-[tex]\mu=np\\\sigma=\sqrt{np(1-p)}[/tex], 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%=0.2Sample size : n=24 [since 1 dozen = 12]Now, the mean and standard deviation of the binomial distribution is given by :-[tex]\mu=24\times0.2=4.8\\\\\sigma=\sqrt{24(0.2)(1-0.2)}\\\\=1.95959179423\approx1.96[/tex]