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

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)`