Question 02 Find the area under the standard normal distribution curve. Also, draw the normal distribution curve and shade the required region;i. To the right of z = 2.01 ii. To the left of z = -1.87 iii. Between z = -2.15 and z = 1.62 Question 03 find the probabilities for each, using the standard normal distribution.i. P(z > 2.33)ii. P(z < -1.51)iii. P(-0.20 < z < 1.56)Question 04 The average number of calories in a 1.5-ounce chocolate bar is 225. Suppose that the distribution of calories is approximately normal with s = 10. Find the probability that a randomly selected chocolate bar will have i. Between 200 and 220 calories ii. Less than 200 calories Question 05 Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are normally distributed with a standard deviation of $1500, find these probabilities.i. The student makes more than $15,000.ii. The student makes between $13,000 and $14,000 Question 06 For a certain group of individuals, the average heart rate is 72 beats per minute. Assume the variable is normally distributed and the standard deviation is 3 beats per minute. If a subject is selected at random, find the probability that the person has the following heart rate.i. Between 68 and 74 beats per minute ii. Higher than 70 beats per minute iii. Less than 75 beats per minute Question 07 The average length of a hospital stay for all diagnoses is 4.8 days. If we assume that the lengths of hospital stays are normally distributed with a variance of 2.1, then 10% of hospital stays are longer than how many days? Thirty percent of stays are less than how many days?Question 08 a. A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds.b. The average overseas trip cost is $2708 per visitor. If we assume a normal distribution with a standard deviation of $405, what is the probability that the cost for a randomly selected trip is more than $3000? If we select a random sample of 30 overseas trips and find the mean of the sample, what is the probability that the mean is greater than $3000?Question 09 The average cholesterol content of a certain brand of eggs is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed.i. If a single egg is selected, find the probability that the cholesterol content will be greater than 220 milligrams.ii. If a sample of 25 eggs is selected, find the probability that the mean of the sample will be larger than 220 milligrams Question 10 a. College students often make up a substantial portion of the population of college cities and towns. State College, Pennsylvania, ranks first with 71.1% of its population made up of college students. What is the probability that in a random sample of 150 people from State College, more than 50 are not college students?b. The percentage of female Americans 25 years old and older who have completed 4 years of college or more is 26.1. In a random sample of 200 American women who are at least 25, what is the probability that at most 50 have completed 4 years of college or more?