6.DETAILSc) What is the probability that X = 31?It is known that 41% of new freshmen at State University will graduate within 6 years. Suppose we take a random sample of n=70 new freshmen at State University. Let X = the number of these sampledfreshmen who graduate within 6 years. (Do not use a normal approximation for this problem. This is a binomial problem.)a) What is the probability that X < 29?b) What is the probability that 28 ≤ x ≤ 31?d) What is the expected value of X?e) What is the variance of X?MY NOTESf) Copy your R script for the above into the text box here.ASK YOUR TEACHER

Let us consider an experiment that has two outcomes only Here, the same experiment has been repeated…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that half of all students (50%) in campus dormitories are dissatisfied with the food service. A random sample of 64 students was taken. What is the probability that the number of students in the sample who were dissatisfied with the food service was between 30 and 34 (inclusive)? (Use the normal approximation to the binomial distribution, without the continuity correction.).
Suppose 22% of students at a certain university are out of state students. A professor takes a random sample of 50 students. Let X = the number of out of state students in the sample. Determine if X is binomial by stating and checking all four requirements. If X is binomial, summarize the distribution of X in shorthand notation.
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 109 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. Probability that fewer than 29 voted The probability that fewer than 29 of 109 eligible voters voted is (Round to four decimal places as needed.)
According to recent data, 45% of the U. S. adults have hypertension. A random sample of 750 adults in the U.S. is selected. Let X represent the number that have hypertension. a. Under what condition will this binomial distribution be bell-shaped? State this condition and verify that that condition is met here. Show the calculation required.
3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.
2) A particular NBA player is a career 59% field goal shooter. If he takes 50 shots, find: a) the probability he makes at most 30 using the normal approximation to the binomial. b) the probability he makes exactly 28 using the normal approximation to the binomial.
2)Assume that the Binomial conditions are met for the values of n and p. A fair die is thrown 10 times and getting a prime number is treated as a success. i. Find the probability of getting a prime number exactly 2 times. ii. Find the probability of getting a prime number at most 2 times. iii. Find mean, variance and standard deviation for getting a prime number.
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 131 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. Probability that fewer than 32 voted
It is known that 37% of new freshmen at State University will graduate within 6 years. Suppose we take a random sample of n=70 new freshmen at State University. Let X = the number of these sampled freshmen who graduate within 6 years. (Do not use a normal approximation for this problem. This is a binomial problem.) a) What is the probability that X < 29? b) What is the probability that 28 ≤ x ≤ 31? c) What is the probability that X = 31? d) What is the expected value of X? e) What is the variance of X?
Q25.If the records show that, the probability of failing (with grade F) this course is p, [use the answer of question 22 above as the probability, p, here], what is the probability that at most 2 students out of 16 fail this course? {Hint: use binomial distribution}
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 111 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. Probability that exactly 26 voted The probability that exactly 26 of 111 eligible voters voted is (Round to four decimal places as needed.)

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