Identify each of the following as rational or irrational.
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Answer:
A Normal approximation to binomial cannot be applied to approximate the distribution of <em>X</em>, the number of computer crashes in a day.
Step-by-step explanation:
Let <em>X</em> = number of computers that will crash in a day.
The probability of a computer crashing in a day is, <em>p </em>= 0.99.
A random sample of <em>n</em> = 131 is selected.
A random computer crashing in a day is independent of the others.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 131 and <em>p</em> = 0.99.
But the sample size is quite large, i.e. <em>n</em> > 30.
So the distribution of <em>X</em> 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:
The second condition is not fulfilled.
A Normal approximation to binomial cannot be applied to approximate the distribution of <em>X</em>, the number of computer crashes in a day.