Question

Assume that x is a binomial random variable with n=600 and p=0.3. Use a normal approximation to find the following probabilities.
a. P (x>180)
b. approximate the probability that x is greater than 70 and less than 90.
c. approximate the probability x = 80

Answer 1

Answer:Given below

Step-by-step explanation:

Given

n=600

probability of success$\left ( p\right ) =0.3$

probability of failure$\left ( q\right )=0.7$

$\left ( a\right )$

$P\left ( x>180\right )=^{600}C_{181}\left ( 0.3\right )^{181}\left ( 0.7\right )^{419}+^{600}C_{182}\left ( 0.3\right )^{182}\left ( 0.7\right )^{418}+^{600}C_{183}\left ( 0.3\right )^{183}\left ( 0.7\right )^{417}+.......+^{600}C_{600}\left ( 0.3\right )^{600}\left ( 0.7\right )^{0}$

$\left ( b\right )$

$P\left ( 70<x<90\right )=^{600}C_{70}\left ( 0.3\right )^{70}\left ( 0.7\right )^{530}+..........+^{600}C_{90}\left ( 0.3\right )^{90}\left ( 0.7\right )^{510}$

$\left ( c\right )$

$P\left ( X=80\right )=^{600}C_{80}\left ( 0.3\right )^{80}\left ( 0.7\right )^{520}$