Question

The 2014 draft picks for the NBA basketball teams have heights that are approximately normally distributed with mean 79.1 inches and standard deviation 3.0 inches. Find the probability that an observation randomly selected from the normal distribution is between 75 inches and 81 inches.

Answer 1

It is given that the mean is 79.1 inches and standard deviation is 3.0 inches so it follows:

$\mu=79.1,\sigma=3$

So the value from 75 to 81 is given by:

$\begin{gathered} P(75\leq x\leq81)=P(x\leq81)-P(x\leq75) \\ =P(z\leq\frac{81-79.1}{3})-P(z\leq\frac{75-79.1}{3}) \\ =P(z\leq0.63)-P(z\leq-1.36) \end{gathered}$

Use the table or a software to get the probability values and substitute to get the probability value as:

The probability is 0.6509.