Answer: P(67 ≤ x ≤ 67.4) = 0.644
Step-by-step explanation:
Since the heights of adult males are approximately normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ/√n
Where
x = the heights of adult males.
µ = mean height
σ = standard deviation
n = number of samples
From the information given,
µ = 66.9 inches
σ = 1.7 inches
n = 50
The probability that their mean height will be between than 67 inches and 67.4 inches is expressed as
P(67 ≤ x ≤ 67.4)
For x = 67,
z = (67 - 66.9)/(1.7/√50) = - 0.42
Looking at the normal distribution table, the probability corresponding to the z score is 0.3372
For x = 67.4,
z = (67.4 - 66.9)/(1.7/√50) = 2.08
Looking at the normal distribution table, the probability corresponding to the z score is 0.9812
Therefore,
P(67 ≤ x ≤ 67.4) = 0.9812 - 0.3372 = 0.644
