Question

Arm span is the physical measurement of the length of an individual's arms from fingertip to fingertip. A man’s arm span is approximately normally distributed with mean of 68 inches with a standard deviation of 3.7 inches. Find length in inches of the 97th percentile for a man’s arm span. Round answer to 2 decimal places

Answer 1

Answer:

The length for the 97th percentile for a man's arm span is 74.96 inches.

Step-by-step explanation:

We have a normal distribution for men's arm span, with mean of 68 inches and standard deviation of 3.7 inches.

The 97th percentil represents the value for which 97% of the observations are below.

We can search for the 97th percentile for the standard normal distribution. This will give a value z=1.88.

Then, we can convert this z-score to our distribution:

$X=\mu+z\cdot\sigma=68+1.88\cdot 3.7=68+6.96=74.96$