- 13-5. Four bad apples are mixed accidentally with 20 good apples Obtain the prohabilin distribution of the mumber of bad apples in a draw of 2 apples at random.
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- Table 1 shows the distribution of the opinions of US adults who are married on how long they could go between jobs without any income and still be able to pay all their bills on time. A researcher believes that the distribution of the US adults who are not married is different from those that are married provided in table 1. The researcher randomly selects 250 US adults who are not married and ask them how long they could go between jobs without any income and still be able to pay their bills on time (Table 2). At alpha =0.01, are the distributions different? Table 1 Response Percentage None 33 One month 15 2 months 11 3 months 7 4 months 4 5 months 3 More than 5 months 25 Not sure 2 Total 100 Table 2 Response Frequency, f None 83 One month 46 2 months 37 3 months 11 4 months 9 5 months 7 More than 5 months 52 Not sure 5 What is the P-value?…A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adult Americar sample proportion of adults who respond yes, is approximately normal, how many more adult Amencans does the.researcher ne (a) 10% of all adult Americans support the changes (b) 15% of all adult Americans support the changes (a) The researcher must ask more American adults. (Round up to the nearest integer) (b) The researcher must ask more American adults (Round up to the nearest integer.)Suppose that a simple random sample of n = 2 numbers will be selected from the list of values 10, 12, 14, 16, 18. (a) There are ten possible equally likely samples of n 2 numbers that could be selected (10 and 12, 10 and 14, etc.). Calculate the sample mean for each sample. = Sample 10, 12 Sample 12, 16 I 10, 14 12, 18 10, 16 14, 16 10, 18 12, 14 14, 18 16, 18 (b) Summarize the results of part (a) into a table showing the sampling distribution of possible sample means. To do this, list each possible value for the sample mean along with the probability the value would occur. (Enter your answers from smallest to largest value for the sample mean.) Probability
- Q1Q4// In how many different ways can eleven cakes be distributed among three kids such that each kid gets not less than two cakes and not more than four cakes?Here is a sample of amounts of weight change (kg) of college students in their freshman year: 13, 7, -3, -5, where -5 represents a loss of 5 kg and positive values represent weight gained. Here are ten bootstrap samples: {13, 13, 13, -3), (13, -5, -3, 13}, {13, 5, 7, 3), (7, 5, 3, 13), {-3, -3, -3, 7}, {7, 5, 7, 5), (13, 7, 5, 3}, {-5, 7, 5, 7), {-5, -3, -5, 7}, {7, 13, 13, 13). Complete parts (a) and (b) below. a. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the mean weight change for the population. (Round to one decimal place as needed.)
- 5) People are waiting in a queue for buying ticket to the cinema. Time required for one person to buy a ticked follows uniform distribution on [2min, 6min]. John arrives to the Cinema 30 minutes before the film starts and there were 10 people waiting in the queue before him. What is the chance that he will be able get his ticket before film starts ?Three groups of children contain respectively 3 girls and I boy: 2 girls and 2 boys: 1 girl and 3 boys. One child is selected at random from each group, Show that the chance that the three selected consist of 1 girl and 2 boys is 13/32?Q2
- Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the number 3. You select two balls at randomandwithoutreplacementfromtheboxandnotethetwonumbersobserved. The sample space S consists of the three equally likely outcomes {(1,2),(1,3),(2,3)} (disregarding order). Let X be the sum of the two balls selected.(a) What is the distribution for X? (b) What is the probability that the sum is at least 4? (c) What is the mean of X?A candy maker offers Child and Adult bags of jelly beans with different color mixes. The company claims that the Child mix has 30% red jelly beans, while the Adult mix contains 15% red jelly beans. Assume that the candy maker’s claim is true. Suppose we take a random sample of 50 jelly beans from the Child mixand a separate random sample of 100 jelly beans from the Adult mix. Let ?^ and ?^ be the sample ??proportions of red jelly beans from the Child and Adult mixes, respectively.a. What is the shape of the sampling distribution of ?^ − ?^ ? Why???b. Find the mean of the sampling distribution. Show your work.c. Find the standard deviation of the sampling distribution. Show your work.