Question

Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes, and the population standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What is the probability that the mean time for the sample of 100 returns for this year is greater than 92?

Multiple Choice

0.4168

Approximately 0

0.0832

0.0764

Answer 1

Solution :

Bones Brothers has maintained careful records the time to prepare a return.  

The mean time to prepare a return is 90 minutes, and the population standard deviation of the distribution is 14 minutes.  

Suppose 100 returns from this year are selected

So n = 100

= 90 minutes , = 14 minutes

We use central limit theorem, thus we assume follows approximately N( 0, 1 ).

To find : P ( > 92 )

P ( > 92 ) =

=

=

=

= 1- P ( Z < 1.43 )....( By using z table )

= 1- 0.9236

P ( > 92 ) = 0.0764

Interpretation :

Probability that the mean time for the sample of 100 returns for this year is greater than 92 is 0.0764