Can someone answer the following problems below and show work.
1. The average diameter of sand dollars on a certain island is 4.00 centimeters with a standard deviation of 0.70 centimeters. If 25 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 3.87 centimeters. Assume that the variable is normally distributed.
2. The average number of mosquitos in a stagnant pond is 70 per square meter with a standard deviation of 8 per square meter. If one square meter of the pond is chosen at random for a mosquito count, find the probability that the average of the count is more than 68 mosquitos per square meter. Assume that the variable is normally distributed.
3. Which of the above two problems (a) or (b) requires application of the Central Limit Theorem? Explain your reasoning.
4. Assume that the mean diastolic blood pressure of normal adults is 80 millimeters of mercury (mm Hg) with a standard deviation of 4.8 mm Hg. Assume that the variable is normally distributed. If a sample of 30 adults is randomly selected, find the probability that the sample mean will be between 80 and 81.4 mm Hg.