Question

The overhead reach distances of adult females are normally distributed with a mean of \( 200 \mathrm{~cm} \) and a standard deviation of \( 8.6 \mathrm{~cm} \). a. Find the probability that an individ

Answer 1

The probability that an individual's overhead reach is within a certain range can be determined using the normal distribution and Z-scores, then looking up the probabilities in a Z-table and finding the difference between them.

Step-by-step explanation:

The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.6 cm. To find the probability that an individual's overhead reach is within a certain range, you would use the normal distribution and calculate Z-scores for the desired endpoints.

Then, using a Z-table or statistical software, you can determine the area (probability) under the curve between those Z-scores.

Suppose you want to calculate the probability that an individual's reach is between 190 cm and 210 cm. First, calculate the Z-scores: Z = (X - mean) / standard deviation.

For X=190 cm, Z = (190-200)/8.6 ≈ -1.16. For X=210 cm, Z = (210-200)/8.6 ≈ 1.16. Look up these Z-scores in a Z-table to find the probabilities for each, and then find the difference between them to get the probability for the range.