Question

Among all the state income tax forms filed in a particular state, the mean income tax paid was μ=$1950 and the standard deviation was σ_X=$490 . As part of a study of the impact of a new tax law, a sample of 100 income tax returns is examined. What is the probability that the sample mean of these 100 returns is greater than $2050? Would this be unusual? Round your probability to four decimal places.

Answer 1

Solution :

= / n = 490 / 100 = 49

P( > 2050) = 1 - P( < 2050)

= 1 - P[( - ) / < (2050 - 1950) / 49]

= 1 - P(z < 2.04)

= 0.0207

Probability = 0.0207

It is unusual