Stat Homework
Stat 104 Chapter 6 Name:________________________
6.2 Homework
page 337-339 #1, 5-13 odd #s, 15, 21, 29, 49, 53, 57, 61
1. State the four requirements for a binomial experiment.
Determine whether the experiment is binomial or not. If the experiment is binomial, identify the random variable X, the number of trials n, the probability of success p, the probability of failure q. If the experiment is not binomial, explain why not.
5. Ask ten of your friends to come to your party (remember the independence assumption).
7. Answer a random sample of eight multiple choice questions either correctly or incorrectly by random guessing. There are four choices, (a) – (d), for each question.
9. Select a student at random in the class until you come across a left-handed student.
11. Four cards are selected at random without replacement from a deck of cards, and the number of queens is observed.
13. Bob has paid to play two games at a carnival. The probability that he wins a particular game is 0.25.
Calculate the probability of X successes for the binomial experiments with the following characteristics:
15. n = 5, p = 0.25, X = 1
21. n = 5, p = 0.25, X ≤ 1
According to the National Center for Education Statistics, business majors accounted for 25% of the proportion of all Master’s degrees granted in 2012. The binomial experiment is to select three Master’s degrees at random and to observe X = number of business majors.
29. Calculate the probability of observing no business majors.
49. For the above situation do the following:
a. Find and interpret the mean µ of X.
b. Calculate the variance ơ2 of X.
c. Compute the standard deviation ơ of X.
53. For the above scenario do the following:
a. Construct the probability distribution graph of X.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
b. Identify the mode of X.
57. Suppose that you are taking a quiz of five multiple choice questions (the instructor chose the questions randomly), with each question having four possible responses. You did not study at all for the quiz and will randomly guess which is the correct response for each question. The random variable X is the number of correct responses.
a. If each question has four possible responses, why is this a valid binomial experiment?
b. State the values of n and p.
c. Calculate the probability that you will pass this quiz by correctly responding to at least three of the five questions. Is this good news for you?
d. Use your answer to part (c) to find the probability that you will not pass the quiz.
61. Referring to problem #57:
a. Compute the mean, variance, and standard deviation of X. Interpret the mean.
b. Use the Z score method to determine which numbers of correct response should be considered outliers,
c. Use technology or the binomial table to construct a probability distribution graph of X. Then state the mode of X, that is, the most likely number of correct responses.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Mode:
d. Find the probability that X = the mode.
Stat 104 6.2 HW
Fall 2020 Instructor J Hodgson Page 1 of 2