Question

Let x be a random variable from a binomial distribution with n = 40 and p = 0.9. If a normal approximation is appropriate, give the distribution of x' that would be used in the approximation.

Answer 1

Answer:

Step-by-step explanation:

Given that x is a random variable from a binomial distribution with n = 40 and p = 0.9.

We find that mean = np= 36 and variance = npq = 3.6

Std dev = square root of variance = 1.897

When we approximate binomial to normal we say

X' is Normal with mean = 36 and std dev = 1.897

X' is N(36, 1.897)

Note:

The condition for binomial approximating to normal is p should be close to 1/2

Here p is 0.9 and also nq=4 is very small.

So normal approximation may not give accurate results.