The heights of all female college basketball players produce a normal distribution with a mean of 68 inches and a standard deviation of 2 inches. The probability that the height of a randomly selected female college basketball player is between 69 and 71 inches is:

Answer: The probability that the height of a randomly selected female college basketball player is between 69 and 71 inches is 0.24

Step-by-step 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