In a school sports day, each student is required to join at least one event. The following table represents theprobability distribution function of the number of events (X) a student takes part in the sports day.X12345P(X = x)0.250.3751.5kk0.05(a) What is the value of k?(b) Find E(X) and o (X).(c) Suppose the number of events students take part are independent. In a group of 6 students, what is theprobability that exactly 4 students join at least 2 events?

Answered: Image /qna-images/answer/725dbd1a-1b41-490e-abe0-b923b9419c1f.jpg

In a school sports day, each student is required to join at least one event. The following table represents the probability distribution function of the number of events (X) a student takes part in the sports day. 2 3 4 5 P(X = x) 0.25 0.375 1.5k k 0.05 (a) What is the value of k? (b) Find E(X) and o (X). (c) Suppose the number of events students take part are independent. In a group of 6 students, what is the probability that exactly 4 students join at least 2 events?

In a school sports day, each student is required to join at least one event. The following table represents the probability distribution function of the number of events (X) a student takes part in the sports day. 2 3 4 5 P(X = x) 0.25 0.375 1.5k k 0.05 (a) What is the value of k? (b) Find E(X) and o (X). (c) Suppose the number of events students take part are independent. In a group of 6 students, what is the probability that exactly 4 students join at least 2 events?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...

See similar textbooks

Similar questions

Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.
If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)
Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.
The sales manager of a company has budgeted K120, 000 for an advertising programme for one of the firm’s product. The selected advertising programme consists of running advertisements in two different magazines. The advertisement for magazine 1 costs K2000 per run while the advertisement for magazine 2 costs K.5000 per run. Past experience has indicated that at least 20 runs in magazine 1, and at least 10 runs in magazine 2 are necessary to penetrate the market with any appreciable effect. Also, experience has indicated that there is no reason to make more than 50 runs in either of the two magazines. How many runs in magazine 1 and how many in magazine 2 should be made? Use simplex method.
A hypothesis test produces a t statistic of t=2.01.If the researcher is using a two tailed test with x=0.05,how large does the sample have to be in order to reject the null hypothesis?
A score that is 2 points higher than the sample mean has a z-score of z = 0.5 and a score of X = 44 has a z-score of -1.00What is the sample mean?
A hypothesis test produces a t statistic of t = 2.30. If the researcher is using a two-tailed test with a = .05, how large does the sample have to be in order to reject the null hypothesis?
The Greer Tire company manufactures a new steel-belted radial tire to be sold through a national chain of discount stores. Because the tire is a new product, Greer’s managers believe that the mileage guarantee offered with the tire will be an important factor in the acceptance of the product. Let X = miles that the tires last: X~N(60,000 2,500) Find the mileage guarantee that ensures this company will repair no more than 15% of its product for free. Assume the distribution of tire mileage is normal.
In the above problem, assume that probability of an item being defective is 0.1. Then in a random sample of 60 such items, how do you apply continuity correction to calculate the probability that at least 5 items are defective? a. P(X is at least 5)=P(X<5.5) b. P(X is at least 5)=P(4.5<X<5.5) c. P(X is at least 5)= P(X>4.5) d. P(X is at least 5)= P(X>5) What are the mean and standard deviation of the binomial in the problem above? a. 6 and 2.32 b. 6 and 5.4 c. 5.4 and 2.32 d. 5.4 and 1.52
As with other products, Fisher-Price faces the decision of how many Weather Teddy units to order for the comingholiday season. Members of the management team suggested order quantities of 15,000, 18,000, 24,000, or28,000 units. The wide range of order quantities suggested indicates considerable disagreement concerning themarket potential. The product management team asks you for an analysis of the stock-out probabilities forvarious order quantities, an estimate of the profit potential, and to help make an order quantity recommendation.Fisher-Price expects to sell Weather Teddy for $24 based on a cost of $16 per unit. If inventory remains afterthe holiday season, Fisher-Price will sell all surplus inventory for $5 per unit. After reviewing the sales historyof similar products, Fisher-Price’s senior sales forecaster predicted an expected demand of 20,000 units with a.95 probability that demand would be between 10,000 units and 30,000 units. Prepare a managerial report that addresses the…
An analyst is interested in knowing whether the proportion of childless couples in a community deviates significantly from the statewide average of 0.12. The analyst suspects a priori that the proportion of childless couples in her community is higher than the statewide average. A sample of 100 couples is interviewed; the mean proportion of childless couples in the sample is found to be 0.16. Test the null hypothesis that the ‘true’ proportion could be 0.12 and give the p-value. Use α = 0.06.
For each of the following scenarios, identify: the population of interest, the outcome variable being measured on each observational unit, whether the outcome variable being measured is categorical or quantitative/Continuous, the parameter of interest, define both in words and using the appropriate statistical symbol (π, π1 -π2, µ, µ1 - µ2, or µd), and the null and alternative hypotheses, written in correct statistical notation (not in words) (a) To examine the safety of working in a nuclear power plant, we assess deaths due to cancer among all deaths at a particular power plant. Based on vital statistics, about 20% of all deaths can be attributed to some form of cancer. (b) A randomized trial study is performed to compare survival (time to death in months) two chemotherapy drugs (A vs B) among cancer patients. A sample of cancer patients are randomly assigned to treatment A or B.