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2. Define sampling with replacement and explain why is it used?4. A psychology class consists of 28 males and 52 females. If the professor selects names from the class list using random sampling,a. What is the probability that the first student selected will be female?b. If a random sample of students is selected and the first two are both females, what is the probability that the third student selected will be male?6. Draw a vertical line through a normal distribution for each of the following z score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body.a. .50b. 0.80c.-0.50d. -0.778. What proportion of a normal distribution is located between each of the following z score boundaries?a. z= -0.25 and z= 0.25b. z= -0.67 and z= 0.67c. z= -1.20 and z= 1.2010. Find the z score location of a vertical line that separates a normal distribution as described in each of the following.a. 5% in the tail on the left.b. 30% in the tail on the right.c. 65% in the body on the left.d. 80% in the body on the right12.A normal distribution has a mean of and a standard deviation of ?. For each of the following scores, indicate whether the tail is to the right or left of the score and find the proportion of the distribution located in the taila.b.c.d.14. For a normal distribution with a mean of and a standard deviation of ?, find the proportion of the population corresponding to each of the following:a. Scores greater than 65b. Scores less than 68c. Scores between 50 and 7016. Iq test scores are standardized to produce a normal distribution with a mean of and a standard deviation of ?. Find the proportion of the population in each of the following iq categories.a. Genius or near genius: iq over 140b. Very superior intelligence: iq from 120-140c. Average or normal intelligence: iq from 90-10918. According to a recent report, people smile an average of a day. Assuming that the distribution of smiles is approximately normal with a standard deviation of ?, find each of the following values.a. What proportion of people smile more than 80 times a day?b. What proportion of people smile at least 50 times a day?20. Rochester, NY averages .19 inches of snow for the month of December. The distribution of snowfall amounts is approximately normal with a standard distribution of ?= 6.5 inches. A local jewelry store advertised a refund of 50% off all purchases made in December if we have more than 3 feet (36 inches) during the month. What is the probability that the jewelry will have to pay off on its promise?22. A true/ false test has 20 questions. If a student is simply guessing answers:a. On average, how many questions would a student answer correctly for the entire test?b. What is the probability that a student would answer more than 15 questions correctly by guessing?c. What is the probability that a student would answer fewer than 7 questions correctly by guessing?24. A test developed to measure ESP involves using Zener cards. Each card shows one of five equally likely symbols ( square, circle, star, cross, wavy lines) and the person being tested has to predict the shape on each card before it is selected. Find each of the probabilities requested for a person who has no ESP and is just guessing.a. What is the probability of correctly predicting exactly 20cards in a series of 100 trials?b. What is the probability that of correctly predicting 10 or more cards in a series of 36 trials?c. What is the probability of correctly predicting more than 16 cards in a series of 64 trials?