Answer: Mean = 4.8
Standard deviation = 1.96
Step-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%=0.2
Sample 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]
