Question

1) One out of every 92 tax returns that a tax auditor examines requires an audit. If 50 returns are selected at random, what is the probability that less than 3 will need an audit? 0.0151 0.9978 0.0109 0.9828

2) Sixty-seven percent of adults have looked at their credit score in the past six months. If you select 31 customers, what is the probability that at least 20 of them have looked at their score in the past six months? 0.142 0.550 0.692 0.450

3) Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line? No, as the probability of six having the correct shape is not unusual Yes, as the probability of six having the correct shape is not unusual No, as the probability of six having the correct shape is unusual Yes, as the probability of six having the correct shape is unusual

Answer 1

Answer 1

Probability that a tax return need an audit = 1/92= 0.011

total number of tax returns = n = 50

we have to find the probability that less than 3 tax return will need an audit, i.e. probability of 0, 1 and 2 audits

Using the binomial probability formula, we can write

setting the values for P(x=0), P(x=1) and P(x=2)

this gives us

And

this gives us

And

this gives us

So, P(less than 3) = P(x=0) + P(x=1) + P(x=2) = 0.5752 + 0.3199 + 0.0872 = 0.9823

This is closest to 0.9828

So, option D is correct answer