Solution:-
a) Standard error of the mean is 12.649.
b) The probability that the sample mean will be less than 130 is 0.293.
x = 130
By applying normal distruibution:-
z = - 0.545
P(z < - 0.545) = 0.293.
c) The probability that the sample mean will be more than 145 is 0.005.
x = 145
By applying normal distruibution:-
z = 2.565
P(z > 2.565) = 0.005.
d) The probability that the sample mean will be between $115 and $155 is 0.882.
x1 = 115
x2 = 155
By applying normal distruibution:-
z1 = - 1.73
z2 = 1.43
P(- 1.73 < z < 1.43) = P(z > - 1.73) - P(z > 1.43)
P(- 1.73 < z < 1.43) = 0.958 - 0.076
P(- 1.73 < z < 1.43) = 0.882
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