Question

Among all the income-tax forms filed in a certain year, the mean tax paid was $2000 and the standard deviation was $500. In addition, for 10% of the forms, the tax paid was greater than $3000. A random sample of 630 tax forms is drawn.

What is the probability that more than 60 of the sampled forms have a tax of greater than $3000?

Answer 1

Solution :

Given, X~Normal(mean=2000, s=500) , n=630 , p=0.1

By using Central Limit Theorem,

So the probability is

P(X>60) = P((X-mean)/s > (60-63)/7.53)

= P(Z> -0.39)

= 0.65173 (check standard normal table)

Thank You.