Im very confused how to solve these problems . Could you explain what steps i need to take ?

Problem #1: Answer by True or False:

a. The central limit theorem applies if sample size n = 20 and the original population is not normal.____________

b. The central limit theorem applies if sample size n = 20 and the original population is normal. ________________

c. The central limit theorem applies if sample size n = 40 and the original population is not normal. _________________

d. The central limit theorem applies if sample size n = 40 and the original population is normal. ____________

Problem #2: In a population of 210 women, the heights of the women are normally distributed with a mean of 64.4 inches and a standard deviation of 2.9 inches. If 36 women are selected at random, find the mean and standard deviation of the population of sample means.

A.64.4 inches, 2.9 inches B.64.4 inches, 2.07 inches

C.64.4 inches, 0.48 inches D.58.8 inches, 2.65 inches

Problem #3:The overhead reach distances of adult females are normally distributed with a mean of 197.5 and a standard deviation of 8.3 cm.(answer part a, b and c. Round to 4 decimals)

a. Find the probability that an individual distance is greater than 210.90 cm.

Show your work: Sketch a normal graph, label the x-axis and shade the corresponding area.

Next: Stat-Calculator-Normal:

mean = Standard deviation =

P( x-------------) = --------------------

b. Find the probability that the mean for 20 randomly selected distances is greater than 196.00 cm.

Show your work: Sketch a normal graph, label the x-axis and shade the corresponding area.

Next: Stat-Calculator-Normal:

mean = Standard deviation =

P( x-------------) = -------------------

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?______________________

Problem #4: The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 9. If 9 fish are randomly selected, what is the probability that the mean weight will be between 17.6 and 23.6 lb? (Round to 4 decimals) DO YOU KNOW HOW TO SHOW YOUR WORK SIMILAR TO THE PREVIOUS EXAMPLE ?????

Problem #5: A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 7.7 hours.

(Round to 4 decimals) DO YOU KNOW HOW TO SHOW YOUR WORK SIMILAR TO THE PREVIOUS EXAMPLE ?????

Problem #6:The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 inches, and a standard deviation of 16 inches. What is the probability that the mean annual precipitation during 64 randomly picked years will be less than 90.8 inches?

A.0.9192 B. 0.4192 C. 0.5808 D. 0.0808

DO YOU KNOW HOW TO SHOW YOUR WORK SIMILAR TO THE PREVIOUS EXAMPLE ?????