STAT 200 STAT200 Quiz 4 Answers (Penn State University)

STAT 200 STAT200 Quiz 4 (Penn State University)

1. Suppose that a student needs to buy 15 books for her history course. The number of books that she will be able to find used is a binomial random variable X with n = 15 and p = 0.30. In other words, the probability that she will find any given book used is 0.30, and is independent from one book to the next. What is the probability that she will find no more than 5 used books?
2. Use software to answer the following: You just found out that you have been kicked out of your apartment (through no fault of your own!) and need to find a new place to live. Suppose monthly rent for an individual is a normally distributed random variable with a mean of 334 dollars and a standard deviation of 22 dollars. What is the probability that you will find an apartment that costs less than 400 dollars per month.
3. Use software to answer the following: You just found out that you have been kicked out of your apartment (through no fault of your own!) and need to find a new place to live. Suppose monthly rent for an individual is a normally distributed random variable with a mean of 334 dollars and a standard deviation of 22 dollars. What is the probability that you will find an apartment that costs more than 400 dollars per month.
4. Correctly identify if the following random variables as either discrete or continuous. The number of new accounts opened at a bank during a certain month
5. Correctly identify whether the following situations satisfy the conditions required to conduct a Binomial experiment. Five percent of all VCRs manufactured by a large electronics company are defective. Three VCRs are randomly selected from the production line of this company. The selected VCRs are inspected to determine whether each of them is defective or good.
6. According to a 2001 study of college students by Harvard University's School of Public Health, 19.3% of those included in the study abstained from drinking (USA TODAY, April 3, 2002). Suppose that of all current college students in the United States, 20% abstain from drinking. A random sample of four college students is selected with the following binomial results:
7. For the given situation, decide if the random variable described is a discrete random variable or a continuous random variable. Random variable X = the weight (in pounds) a dieter will lose after following a two week weight loss program.
8. The probability distribution for X = number of heads in 4 tosses of a fair coin is given in the table above. What is the value of the cumulative distribution function at 3, i.e. P(X ≤ 3)?
9. Sara is a frequent business traveler. For security purposes, 10% of all people boarding airplanes are randomly selected for additional screening just prior to boarding. What is the probability that the first time Sara is selected for screening is on her third flight?
10. Suppose that for X = net amount won or lost in a lottery game, the expected value is E(X) = -$0.50. What is the correct interpretation of this value?
11. The probability is p = 0.80 that a patient with a certain disease will be successfully treated with a new medical treatment. Suppose that the treatment is used on 40 patients. What is the expected value of the number of patients who are successfully treated?
12. For a normal random variable (Using Standard Normal Table), the probability of an observation being less than the median is:
13. Using Standard Normal Table, find the probability that a z-score is less than -2.56 or greater than 1.51.
14. Using Standard Normal Table, what is the probability that Z is between -1 and 1, P(-1 < Z < 1)?
15. The time taken for a computer to boot up, X, follows a normal distribution with mean 30 seconds and standard deviation 5 seconds. What is the standardized score (z-score) for a boot-up time of x =20 seconds?
16. [Fill in the blank] Ellen is taking 4 courses for the semester. She believes that the probability distribution function for X = the number of courses for which she will get an A grade is given above. What is the expected number of A’s she will get? E(X) = ________ A's