Question 02Find the area under the standard normal distribution curve. Also, draw the normaldistribution curve and shade the required region;i. To the right of z = 2.01ii. To the left of z = -1.87iii. Between z = -2.15 and z = 1.62Question 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 04The average number of calories in a 1.5-ounce chocolate bar is 225. Suppose thatthe distribution of calories is approximately normal with s = 10. Find the probabilitythat a randomly selected chocolate bar will havei. Between 200 and 220 caloriesii. Less than 200 caloriesQuestion 05Full-time Ph.D. students receive an average of $12,837 per year. If the average salariesare 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 $14,000Question 06For a certain group of individuals, the average heart rate is 72 beats per minute. Assumethe variable is normally distributed and the standard deviation is 3 beats per minute. Ifa subject is selected at random, find the probability that the person has the followingheart rate.i. Between 68 and 74 beats per minuteii. Higher than 70 beats per minuteiii. Less than 75 beats per minuteQuestion 07The average length of a hospital stay for all diagnoses is 4.8 days. If we assume that thelengths of hospital stays are normally distributed with a variance of 2.1, then 10% ofhospital stays are longer than how many days? Thirty percent of stays are less than howmany days?Question 08a. A survey found that the American family generates an average of 17.2 pounds ofglass garbage each year. Assume the standard deviation of the distribution is 2.5pounds. Find the probability that the mean of a sample of 55 families will bebetween 17 and 18 pounds.b. The average overseas trip cost is $2708 per visitor. If we assume a normaldistribution with a standard deviation of $405, what is the probability that the costfor a randomly selected trip is more than $3000? If we select a random sample of30 overseas trips and find the mean of the sample, what is the probability that themean is greater than $3000?Question 09The average cholesterol content of a certain brand of eggs is 215 milligrams, and thestandard deviation is 15 milligrams. Assume the variable is normally distributed.i. If a single egg is selected, find the probability that the cholesterol content willbe greater than 220 milligrams.ii. If a sample of 25 eggs is selected, find the probability that the mean of thesample will be larger than 220 milligramsQuestion 10a. College students often make up a substantial portion of the population of collegecities and towns. State College, Pennsylvania, ranks first with 71.1% of itspopulation made up of college students. What is the probability that in a randomsample 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 completed4 years of college or more is 26.1. In a random sample of 200 American womenwho are at least 25, what is the probability that at most 50 have completed 4 yearsof college or more?