Answer: The probability that the height of a randomly selected female college basketball player is between 69 and 71 inches is 0.24
Explanation:
Since the heights of all female college basketball players produce a normal distribution, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = heights of all female college basketball players.
µ = mean height
σ = standard deviation
From the information given,
µ = 68 inches
σ = 2 inches
We want to find the probability that the height of a randomly selected female college basketball player is between 69 and 71 inches is expressed as
P(69 ≤ x ≤ 75)
For x = 69,
z = (69 - 68)/2 = 0.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.6915
For x = 71,
z = (71 - 68)/2 = 1.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.9332
Therefore,
P(69 ≤ x ≤ 75) = 0.9332 - 0.6915 = 0.24