Question

1. The CPA Practice Advisory reports that the mean preparation fee for Federal Income tax returns was $273 in 2017 with a population standard deviation of $100.

a) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

b) What is the probability that the mean of a sample of 50 tax returns is more than $289?                

Answer 1

Solution :

Given that ,

mean = = 273

standard deviation = = 100

a ) n = 30

=   = 273

= / n = 100/ 30 = 18.2574

within 16 = 273  ± 16 = 257, 289

P(257 < < 138)  

= P[(257 - 273) / 18.2574< ( - ) / < (289 - 273) /18.2574 )]

= P(-0.88 < Z < 0.88)

= P(Z < 0.88) - P(Z < -0.88)

Using z table,  

= 0.8106 - 0.1894

= 0.6212

Probability = 0.6212

b ) n = 50

=   = 273

= / n = 100/ 50 = 14.1421

P (x > 289 )

= 1 - P (x < 289 )

= 1 - P ( - ) / ) < ( 289 - 273 / 14.1421)

= 1 - P ( z < 16 / 14.1421 )

= 1 - P ( z < 1.13 )

Using z table

= 1 - 0.8708

= 0.1292

Probability = 0.1292