Solve the problem.
-The weights of the fish in a certain lake are normally distributed with a mean of 12 lb and a standard deviation of 12. If 16 fish are randomly selected, what is the probability that the mean weight will be between 9.6 and 15.6 lb?
A)0.3270
B)0.0968
C)0.6730
D)0.4032

Question

Quizplus · Accepted Answer

Using the Central Limit Theorem, we can calculate the probability that the mean weight of 16 randomly selected fish falls between 9.6 and 15.6 pounds. The standard error (SE) of the mean is the standard deviation divided by the square root of the sample size, which is $12 / \sqrt{16} = 3$. We then convert the weights into z-scores: $Z_1 = (9.6 - 12) / 3 = -0.8$ and $Z_2 = (15.6 - 12) / 3 = 1.2$. Looking up these z-scores in a standard normal distribution table gives us the probabilities of 0.2119 and 0.8849, respectively. The probability that the mean weight is between 9.6 and 15.6 lb is the difference, 0.8849 - 0.2119 = 0.6730.

Solve the Problem. -The Weights of the Fish in a Certain Lake Are