If the heights of NBA players are normally distributed with a mean height of 73.5 inches and a standard deviation of 2.2 inches, what is the probability of randomly selecting an NBA player who is between 72 and 73 inches tall?
A) 0.1624
B) 0.5910
C) 0.4500
D) 0.4090

Question

Quizplus · Accepted Answer

To find the probability of a player being between 72 and 73 inches tall, we use the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For 72 inches, Z = (72 - 73.5) / 2.2 = -0.6818. For 73 inches, Z = (73 - 73.5) / 2.2 = -0.2273. Looking these Z-scores up in a standard normal distribution table or using a calculator, we find the probabilities for each and subtract the smaller from the larger to find the probability of being between these two heights. The calculation gives us approximately 0.1624, indicating the probability is 16.24%.

If the Heights of NBA Players Are Normally Distributed with a Mean