Question

A die is rolled 360 times. Let say that you want to use normal approximation to find the probability that the number of 4 was rolled exactly 100 times. You need to find the probability that X=100. Explain how you would use continuity correction in this case.

Answer 1

0.0000

Explanation:

Given that a die is rolled 360 times. Let say that you want to use normal approximation to find the probability that the number of 4 was rolled exactly 100 times.

Here we know that getting 4 is binomial with p = 1/6 and n =360

By approximating to normal after checking conditions are satisfied we have

X = no of fours obtained is normal

with mean =
`np =60`

and variance =
`npq = 50`

Std dev = 7.072

X is N(60, 7.072)

For finding out prob x=100 we have to do continuity correction as

`P(X=100) = P(99.5<x<100.5)\\\\=P((99.5-60)/(7.072) \\=P(5.585<z<5.73)\\\\=0.000`