Assume that x is a binomial random variable with n = 100 and p = 0.60. Use a normal approximation to find P(x

Question

Assume that x is a binomial random variable with n = 100 and p = 0.60. Use a normal approximation to find P(x < 65).
A) 0.8212
B) 0.8686
C) 0.5753
D) 0.1788

Quizplus · Accepted Answer

The normal approximation to the binomial distribution is valid when np and n(1-p) are both greater than or equal to 5. In this case, np = 100 * 0.60 = 60 and n(1-p) = 100 * 0.40 = 40, so the normal approximation is valid.The mean of the binomial distribution is np = 60 and the standard deviation is sqrt(np(1-p)) = sqrt(60 * 0.40) = 4.90.Therefore, P(x < 65) = P(z < (65 - 60) / 4.90) = P(z < 1.02) = 0.8413.

Assume That X Is a Binomial Random Variable with N