Question

It has been found that times taken by people to complete a particular tax form follow a normal distribution with mean 100 minutes and standard deviation 30 minutes. A random sample of nine people who have completed this tax form was taken. What is the probability that the sample mean time taken is more than two hours?

Answer 1

I found this online hold on

Answer 2

It has been found that times taken by people to complete a particular tax form follow a normal distribution with mean 100 minutes and standard deviation 30 minutes.
(a) What is the probability that a randomly chosen person takes less than 85 minutes to complete this form?

Answer 3

P(x<85)=P(Z<(85-100)/30)

Answer 4

=P(Z<-0.5)
=P(Z>0.5) because of the negative
=1-(0.5+0.1915)
=0.3085

Answer 5

so we would do the same thing we did for this example except that we would change x<85 into more than two hours

Answer 6

and two hours equal 120 minutes therefore the equation would be x>2 or 2<x

Answer 7

But the question from @b77w asks for the probability of the sample mean time taken being more than 120 minutes, where the sample size is nine people. So, the solution needs to take account of the sample size.

Answer 8

The solution can be found from the following relationship:
\[\large \frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}}\ distribution\ N(0,1) \]

Answer 9

i got .0228, does that sound right?

Answer 10

Yes, I got 0.0228 as well!