Respuesta :
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:
[tex]np=131\times 0.99=129.69>10\\n(1-p)=131\times (1-0.99)=1.31<10[/tex]
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.
