Answer: P(x > 71.7) = 0.002
Explanation:
Since the heights of the men are assumed to be normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = heights of the men.
µ = mean height
σ = standard deviation
From the information given,
µ = 70.7 inches
σ = 2.1 inches
The probability that they have a mean height greater than 71.7 inches is expressed as
P(x > 71.7) = 1 - P(x ≤ 71.7)
For x = 71.7
Since n = 36, then
z = (71.7 - 70.7)/2.1/√36 = 2.86
Looking at the normal distribution table, the probability corresponding to the z score is 0.998
P(x > 71.7) = 1 - 0.998 = 0.002