It is known that 37% of new freshmen at State University will graduate within 6 years. Suppose we take a randomsample of n=70 new freshmen at State University. Let X = the number of these sampled freshmen who graduatewithin 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?

Answered: It is known that 37% of new freshmen at…

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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5 Show that mean of the binomial distribution is the product of the parameter p and the number of times n.
In a lottery, the top cash prize was $644 million, going to three lucky winners. Players pick five different numbers from 1 to 52 and one number from 1 to 42. A player wins a minimum award of $100 by correctly matching two numbers drawn from the white balls (1 through 52) and matching the number on the gold ball (1 through 42). What is the probabilit of winning the minimum award? The probability of winning the minimum award is (Type an integer or a simplified fraction.)
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.).
Assume that the Binominl 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 succens, 1-Find the probability of getting a prime number exactly 2 times, 2-Find the probability of getting a prime number at most 2 times. 3-Find mean, variance and standard deviation for getting a prime number.
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.
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.
A law professor observed that only 20% of the students who get admitted to the freshmen class usually reached fourth year. Assuming that this is correct, find the probability that among 15 randomly selected first year students, exactly 3 students will reach fourth year?
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.
6. DETAILS c) 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 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? d) What is the expected value of X? e) What is the variance of X? MY NOTES f) Copy your R script for the above into the text box here. ASK YOUR TEACHER
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.
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}

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