A group of boys at GHS had their heights measured. The mean height was determined to be 68 inches with a standard deviation of 3 inches . If one of these boys is selected at random, what is the probability that he will be less than 65 inches tall? .34 .66 .84 .16

## Step 1: Calculate the z-score<br />### The z-score measures how many standard deviations a data point is from the mean. It is calculated as: $z = \frac{x - \mu}{\sigma}$, where $x$ is the data point (65 inches), $\mu$ is the mean (68 inches), and $\sigma$ is the standard deviation (3 inches). Therefore, $z = \frac{65 - 68}{3} = -1$.<br /><br />## Step 2: Find the probability corresponding to the z-score<br />### A z-score of -1 corresponds to a probability of 0.1587 (from a standard normal distribution table or calculator). This represents the probability of a randomly selected boy being shorter than 65 inches. Rounding to the nearest hundredth gives 0.16.