Question

Compute P(x) using the binomial probability formula. Then determine whether the normal distribution can be used as an approximation for the binomial distribution. If so, approximate P(x) and compare the result to the exact probability.

n = 50, p = 0.5, x = 25

Answer 1

Thursday

30/07/2020

1) Binomial probability distributions Given 2) Givena Given = Approximate probability is greater than exact probability by 0.001 p= 0.5 ne 50 H = 25 3) Approximate P(X) using normal distribution = Given = n = 50 p= 0.5 4 = 1-p = 0.5 ne 50 P=0.5 O = 3.5355 PIX = 25) = np 1-pl PC between 24.5 and 25.5 → Here, P[24.5<x<25.5 = = 50025 * (0.5)^25 (1-0.5)450-25 = 126410606437752 *o *(0.5)-25 = 0.1123 = 50*0.5*0.5 = 12.5 = пр = 50*0.5 = 25 = P(25.5-25/3.5355 <-u/o < 24.5-25/3.5355) Here, 12.5_>10 = P(0.1414 <z<-0.1414) = Vnpa = 150*0.5*0.5 = 3.5355 = P(Z<0.1414) - PIZ-0.1414) Option D Hence, the above condition is satisfied so, the normal distribution can be used to approximate the probability. = 0.5562 -0.4438 .....(from standard normal distribution table) = 0.1124