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.
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
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