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Answer:
a) Since the distribution is normal, the distance from the mean to the upper limit is going to be the same as the distance from the mean to the lower limit. The mean is going to be the mid point between the limits, which is going to be the average of the limits. The limits are going to have a z score associated, in this case the upper z is 1.96 and the lower z is -1.96 as shown in the picture.
(4.4 + 6.0)/2 = 5.2
The mean for men is going to be 5.2 million cells/uL
b) The standard deviation for men can be calculated using the z score and the limit values. The formula is shown in the picture.
σ = (6.0 - 5.2)/1.96 = 0.4
The standard deviation is 0.4 million cells/uL
