Solution :
Given that,
mean = = 69
standard deviation = = 14
n = 12
The sampling distribution of mean is ,
= = 69
The sampling distribution of standard deviation is ,
= / n = 14 / 12 = 4.0415
b)
P(x 72.3)
= P[(x - ) / (72.3 - 69) /4.0415 ]
= P(z 0.82)
= 0.7939
probability = 0.7939
c)
P(x 70.2 ) = 1 - P(x 70.2)
= 1 - P[(x - ) / (70.2 - 69) /4.0412 ]
= 1 - P(z 0.30 )
= 1 - 0.6179 = 0.3821
probability = 0.3821
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