a For classes of 299 students find the mean and standard dev

a. For classes of 299 students, find the mean and standard deviation for the number born on the 4th of July. Ignore leap years.

Solution:

Problem on binomal distribution.

Binomial with n = 299

p=Probability of success= P(born on July 4th ) = 1/365 =2.739*10^-3

q=probability of failure =1-p = 1 -2.739*10^{-3 =} 0.9973

Mean with finite trials n in binomial distribution is given by the formula

mean = np =299 *2.739*10^-3

⁼0.8189

standard deviation is given in binomial distribution is given by

standard deviation=square root(npq)

=square root(299 *2.739*10^-3 *0.9973)

=0.9037