5.2 STATISTICS HOMEWORK - BIONOMIAL PROBABILITY DISTRIBUTIONS

Assume that a procedure yields a binomial distribution with n=4 trials and a probability of success of p=0.90. Use a binomial probability table to find the probability that the number of successes x is exactly 1.

0.004 (from table)

Assume that random guesses are made for 8 ​multiple-choice questions on a test with 2 choices for each​ question, so that there are n=8 ​trials, each with probability of success​ (correct) given by p=0.50. Find the probability of no correct answers.

0.004 (from table)

If calculations are​ time-consuming and if a sample size is no more than​ 5% of the size of the​ population, the​ _______ states to treat the selections as being independent​ (even if the selections are technically​ dependent).

5% Guideline for Cumbersome Calculations

Assume that when adults with smartphones are randomly​ selected, 36​% use them in meetings or classes. If 8 adult smartphone users are randomly​ selected, find the probability that exactly 4 of them use their smartphones in meetings or classes.

P(x=4)=binompdf(8, 0.36, 4) = 0.1973

Assume that when adults with smartphones are randomly​ selected, 54​% use them in meetings or classes. If 7 adult smartphone users are randomly​ selected, find the probability that at least 4 of them use their smartphones in meetings or classes.

P(x=4,5,6,7) = binompdf(7,0.54,4)+binompdf(7,0.54,5)+binompdf(7,0.54,6).... = 0.587

Which of the following is not a requirement of the binomial probability distribution?

The trails must be dependent

Determine whether the given procedure results in a binomial distribution​ (or a distribution that can be treated as​ binomial). If the procedure is not​ binomial, identify at least one requirement that is not satisfied. The YSORT method of sex​ selection, developed by the Genetics​ & IVF​ Institute, was designed to increase the likelihood that a baby will be a boy. When 140 couples use the YSORT method and give birth to 140 ​babies, the sex of the babies is recorded.

Yes, because the procedure satisfies all the criteria for a binomial distribution

A Gallup poll of 1236 adults showed that​ 12% of the respondents believe that it is bad luck to walk under a ladder. Consider the probability that among 30 randomly selected people from the 1236 who were​ polled, there are at least 2 who have that belief. Given that the subjects surveyed were selected without​ replacement, the events are not independent. Can the probability be found by using the binomial probability​ formula? Why or why​ not?

Yes. Although the selections are not​ independent, they can be treated as being independent by applying the​ 5% guideline.

Based on a​ poll, among adults who regret getting​ tattoos, 12​% say that they were too young when they got their tattoos. Assume that four adults who regret getting tattoos are randomly​ selected, and find the indicated probability. a. Find the probability that none of the selected adults say that they were too young to get tattoos. b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos. c. Find the probability that the number of selected adults saying they were too young is 0 or 1. d. If we randomly select four ​adults, is 1 a significantly low number who say that they were too young to get​ tattoos? ______ because the probability that ______ of the selected adults say that they were too young is ________ 0.05.

a. 0.5997 - binompdf(4,.12,0) b. 0.3271 - binompdf(4,.12,1) c. 0.9268 - 0.5997+0.3271 d. No, at most 1, greater than

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a​ girl, but assume that the method has no​ effect, so the probability of a girl is 0.5.Assume that the groups consist of 46 couples. a. The mean is _______. The st. dv. is _______. b. Use the range rule of thumb to find the values separating the results that are significantly low or significantly high. c. Is the result of 35 girls a result that is significantly​ high? What does it suggest about the effectiveness of the​ method?

a. 23 - np =(46)(0.5); 3.4 - squareroot (46)(0.5)(0.5) b. 16.2 low value - 23-2(3.4); 29.8 high value - 23+2(3.4) c. The result IS significantly high, because 35 girls is GREATER THAN 29.8 girls. A result of 35 girls would suggest that the method IS EFFECTIVE.

a. Use the multiplication rule to find ​P(WCC​), where C denotes a correct answer and W denotes a wrong answer.

a. P(W)P(C)P(C) = (0.20)(0.80)(0.80) = 0.032 b. 0.032; 0.032 c. 0.032+0.032+0.032 = 0.096

Assume that hybridization experiments are conducted with peas having the property that for​ offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 20. a. the mean is _____. The st. dev. is ______. b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. c. Is a result of 2 peas with green pods a result that is significantly​ low? Why or why​ not?

a. mean = 15 - (20)(0.75); st. dev. = 1.9 - square root (20)(0.75)(0.25) b. 11.2 low value; 18.8 high value c. The result IS significantly low, because 2 peas with green pods is LESS THAN 11.2 peas.

Identify the expression for calculating the mean of a binomial distribution.

np

In the binomial probability​ formula, the variable x represents the​ _______.

number of successes

For the binomial​ distribution, which formula finds the standard​ deviation?

square root of npq

Determine whether the given procedure results in a binomial distribution. If it is not​ binomial, identify the requirements that are not satisfied. Treating 20 bald men with a special shampoo and recording how they say their scalp.

No, because there are more than two possible outcomes

Determine whether or not the procedure described below results in a binomial distribution. If it is not​ binomial, identify at least one requirement that is not satisfied. Five hundred different voters in a region with two major political​ parties, A and​ B, are randomly selected from the population of 8500 registered voters. Each is asked if he or she is a member of political party​ A, recording Yes or No.

No, the trails are not independent and the sample is more than 5% of the population.

Determine whether the given procedure results in a binomial distribution​ (or a distribution that can be treated as​ binomial). If the procedure is not​ binomial, identify at least one requirement that is not satisfied. Eight different senators from the current U.S. Congress are randomly selected without replacement and whether or not​ they've served over 2 terms is recorded. Does the probability experiment represent a binomial​ experiment?

No, because the trails of the expirement are not independent and the probability of success differs from trial to trial