Question

question 16
1 pts
the weights of individuals in a population vary according to a normal distribution with a mean of 145 pounds and a standard deviation of 18 pounds. approximately 25% of the individuals in this population weigh more than
150 pounds
170 pounds
199 pounds
163 pounds
158 pounds

Explanation:

Step1: Find the z - score

We know that if approximately 25% of the individuals weigh more than a certain value, then 75% weigh less. Looking up the z - score in the standard normal distribution table for a cumulative probability of 0.75, the z - score \(z\approx0.67\).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the value we want to find, \(\mu\) is the mean, and \(\sigma\) is the standard deviation. We know \(\mu = 145\), \(\sigma=18\), and \(z = 0.67\). Rearranging the formula for \(x\) gives \(x=\mu+z\sigma\).

Step3: Calculate \(x\)

Substitute the values into the formula: \(x = 145+0.67\times18=145 + 12.06=157.06\approx158\) pounds.

Answer:

158 pounds