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

To find the length in inches of the 97th percentile for a man’s arm span, calculate the z-score corresponding to the percentile and use it to find the corresponding value in the standard normal distribution.

Step-by-step explanation:

To find the length in inches of the 97th percentile for a man’s arm span, we need to calculate the z-score corresponding to the 97th percentile and use it to find the corresponding value in the standard normal distribution. The z-score can be calculated using the formula: z = (x - mean) / standard deviation. Substituting the given values into the formula, we get: z = (x - 68) / 3.7. Solving for x, we get x = z * 3.7 + 68. To find the value at the 97th percentile, we can use a z-score lookup table or a calculator that provides the value directly. The z-score corresponding to the 97th percentile is approximately 1.8808. Substituting this value into the formula, we get x = 1.8808 * 3.7 + 68, which gives us a value of approximately 75.96 inches. Therefore, the length in inches of the 97th percentile for a man’s arm span is approximately 75.96 inches.

Answer 2

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`