Question

The weights of salmon in the Sacramento River are normally distributed with a mean of 20 pounds and a standard deviation of 8 pounds. What percent of salmon have weights less than 9.8 pounds?

If there are two answers, list both answers separated by a comma.

Answer 1

To find the percent of salmon that have weights less than 9.8 pounds, we calculate the z-score and find the area under the standard normal distribution curve.

Step-by-step explanation:

To find the percent of salmon that have weights less than 9.8 pounds, we need to calculate the z-score corresponding to this weight and then find the area under the standard normal distribution curve to the left of this z-score.

The formula to calculate the z-score is: z = (x - mean) / standard deviation. Substituting the given values, we get: z = (9.8 - 20) / 8 = -1.775.

Using a standard normal distribution table or calculator, we can find that the area to the left of -1.775 is approximately 0.0381 or 3.81%.