Solution :
Given that,
mean = = 277500
standard deviation = = 21500
n = 250
= 277500
= / n = 21500 / 250 = 1359.7794
a) The distribution of the sample mean = 277500
The standard deviation of the sample mean = 1359.7794
b) P( > 282500 ) = 1 - P( < 282500)
= 1 - P[( - ) / < ( 282500 - 277500) / 1359.7794 ]
= 1 - P(z < 3.677)
Using z table,
= 1 - 0.9999
= 0.0001
Probability = 0.0001
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