Question

Consider the probability that greater than 77 out of 131 computers will crash in a day. Assume the probability that a given computer will crash in a day is 99%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

Answer 1

Answer:

A Normal approximation to binomial cannot be applied to approximate the distribution of X, the number of computer crashes in a day.

Step-by-step explanation:

Let X = number of computers that will crash in a day.

The probability of a computer crashing in a day is, p = 0.99.

A random sample of n = 131 is selected.

A random computer crashing in a day is independent of the others.

The random variable X follows a Binomial distribution with parameters n = 131 and p = 0.99.

But the sample size is quite large, i.e. n > 30.

So the distribution of X can be approximated by the normal distribution if the following conditions are fulfilled:

• np ≥ 10
• n(1 - p) ≥ 10

Check whether the conditions satisfy or not:

$np=131\times 0.99=129.69>10\\n(1-p)=131\times (1-0.99)=1.31$

The second condition is not fulfilled.

A Normal approximation to binomial cannot be applied to approximate the distribution of X, the number of computer crashes in a day.