must show all work

central limit theory, ( Please show all work)

1. The weights of the fish in a certain lake are normally distributed with a mean of 19 pounds and a standard deviation of 6. If 4 fish are randomly selected, what is the probability that the mean weight will be between 16.6 and 22.6 pounds.

    

2. Assume that a woman's height are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 90 women are randomly selected, Finder probability that they have a mean height between the 62.9 inches and 64.0 inches.

    

    

3. For women aged 18 - 24, systolic blood pressure are normally distributed (in mm Hg) are normally distributed with a mean of 14.8 and a standard deviation of 13.1. If 23 women aged 18 through 24 are randomly selected, Finder probability that there means systolic blood pressure is between 119 and 122.

1.  Find the critical value Z a/2 that corresponds to a 93% confidence level.

    

    

2. 12. find Za/2 for a = 0.09