Answer: P(33 ≤ x ≤ 41) = 0.34
Explanation:
Since the number of times a group of middle aged men have been to the gym in the past year is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = number of times.
µ = mean
σ = standard deviation
From the information given,
µ = 33 times
σ = 8 times
The probability that the men have been to the gym between 33 to 41 times is expressed as
P(33 ≤ x ≤ 41)
For x = 33
z = (33 - 33)/8 = 0
Looking at the normal distribution table, the probability corresponding to the z score is 0.5
For x = 41
z = (41 - 33)/8 = 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.84
P(33 ≤ x ≤ 41) = 0.84 - 0.5 = 0.34