Question

The weights of the fish in a certain lake are normally distributed with a mean of 10 lb and a standard deviation of 6. If 4 fish are randomly selected, what is the probability that the mean weight will be between 7.6 and 13.6 lb?

A) 0.3849
B) 0.6151
C) 0.7697
D) 0.2303

Answer 1

To find the probability that the mean weight will be between 7.6 and 13.6 lbs, we need to calculate the z-scores corresponding to these values and then use the standard normal distribution table. The probability is approximately 0.6151.

Step-by-step explanation:

To find the probability that the mean weight will be between 7.6 and 13.6 lbs, we need to calculate the z-scores corresponding to these values and then use the standard normal distribution table. First, we calculate the z-score for 7.6 lbs: z = (7.6 - 10) / (6 / sqrt(4)) = -0.8. Next, we calculate the z-score for 13.6 lbs: z = (13.6 - 10) / (6 / sqrt(4)) = 1.2. Using the standard normal distribution table, we find that the probability of a z-score between -0.8 and 1.2 is approximately 0.6151.