Question

the weights of fish in a certain lake are normaly distributed with a mean of 9.1 lb and an SD of 1.7. if 70 fish are randomly selected, what is the probability that the mean weight will be less than 10.6lb?

Answer 1

Let X lbs be the the weight of any given fish. X is normally distributed with a mean of lb and an SD of .

Let be the mean weight of a randomly selected sample of n=70 fish. Since the sample size n=70 is greater than 30, using the central limit theorem, we can say that the sampling distribution of mean is normally distributed. That is, we can say that is normally distributed with mean and standard deviation (also called standard error of mean)

if 70 fish are randomly selected, The probability that the mean weight (which is ) will be less than 10.6lb is

ans:  if 70 fish are randomly selected, The probability that the mean weight will be less than 10.6lb is 1.0000