Please show me the work so that I can understand. I have had trouble with these problems all week. Thank you.

The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution, as shown in the figure. (a) What is the minimum UGPA that would still place a student in the top 5% H = 3.40 of UGPAs? 630.16 (b) Between what two values does the middle 50% of the UGPAs lie? X 2.8 3.40 Grade point averageThe red blood cell counts [in millions. of cells per microliter]: for a population of adult melee can be approximated by a normal distribution. with a mean of 5.? million cells per microliter and a standard deviation oft}.5 million cells per microliter. [a] What is the minimum red blood cell count that can he in the top 21% of counts? [b] What is the maximum red blood cell count that can he in the bottom 13% of counts? The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n = 60, find the probability of a sample mean being less than 21.1 if p = 21 and o = 1.18.The heights of fully grown trees of a specific species are normally distributed, with a mean of 52.0 feet and a standard deviation of 5.00 feet. Random samples of size 14 are drawn from the population. Use the central limit theorem to find the mean and standard error of the sampling distribution. Then sketch a graph of the sampling distribution. The mean of the sampling distribution is H- = The standard error of the sampling distribution is of = (Round to two decimal places as needed.)Find the probability and interpret the results. If convenient, use technology to find the probability. The population mean annual salary for environmental compliance specialists is about $63,000. A random sample of 31 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $60,500? Assume o = $5,600. The probability that the mean salary of the sample is less than $60,500 is (Round to four decimal places as needed. )The mean height of women in a country (ages 20 - 29) is 64.1 inches. A random sample of 75 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume 6 =2.71. The probability that the mean height for the sample is greater than 65 inches is (Round to four decimal places as needed.)The height of women ages 20-29 is normally distributed, with a mean of 64.4 inches. Assume o = 2.4 inches. Are you more likely to randomly select 1 woman with a height less than 66.5 inches or are you more likely to select a sample of 11 women with a mean height less than 66.5 inches? Explain. Click the icon to view page 1 of the standard normal table. Click the icon to view page 2 of the standard normal table. What is the probability of randomly selecting 1 woman with a height less than 66.5 inches? (Round to four decimal places as needed.)The lengths of lumber a machine cuts are normally distributed with a mean of 90 inches and a standard deviation of 0.7 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 90.19 inches? (b) A sample of 41 boards is randomly selected. What is the probability that their mean length is greater than 90.19 inches?The weights of ice cream cartons are normally distributed with a mean weight of 12 ounces and a standard deviation of 0.5 ounce. (a) What is the probability that a randomly selected carton has a weight greater than 12.18 ounces? (b) A sample of 16 cartons is randomly selected. What is the probability that their mean weight is greater than 12. 18 ounces