Describe the key similarity between a binomial distribution and a hypergeometric distribution. both distributions involve a uniform probability both distributions involve independent trials both distributions involve counting successes in a given number of trials both distributions involve dependent trials
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![Describe the key similarity between a binomial distribution and a hypergeometric distribution.
both distributions involve a uniform probability
both distributions involve independent trials
both distributions involve counting successes in a given nunmber of trials
both distributions involve dependent trials
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- Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 30 and p = 0.40. (For each answer, enter a number. Use 2 decimal places.)n·p = n·q = Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____, p̂ _____ be approximated by a normal random variable because _____ _____.first blank YesNo second blank cancannot third blank n·q exceedsn·p does not exceed n·p exceedsboth n·p and n·q exceedn·q does not exceedn·p and n·q do not exceed fourth blank (Enter an exact number.)What are the values of ?p̂ and ?p̂? (For each answer, enter a number. Use 3 decimal places.)?p̂ = mu sub p hat = ?p̂ = sigma sub p hat = (b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____,…Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 35 and p = 0.32. (For each answer, enter a number. Use 2 decimal places.)n·p = n·q = Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____, p̂ _____ be approximated by a normal random variable because _____ _____.first blank YesNo second blank cancannot third blank n·q exceedsn·p exceeds n·p and n·q do not exceedboth n·p and n·q exceedn·p does not exceedn·q does not exceed fourth blank (Enter an exact number.)What are the values of ?p̂ and ?p̂? (For each answer, enter a number. Use 3 decimal places.)?p̂ = mu sub p hat = ?p̂ = sigma sub p hat = (b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____, p̂…Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 35 and p = 0.28. (For each answer, enter a number. Use 2 decimal places.)n·p = n·q = Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____, p̂ _____ be approximated by a normal random variable because _____ _____.
- Lawrence likes to shoot a bow and arrow in his free time. On any shot, he has about a 10% chance of hitting the bull's-eye. As a challenge one day, Lawrence decides to keep shooting until he gets a bull's-eye. Let Y = the number of shots he takes. Does this scenario describe a binomial setting? Justify your answer. Yes, this is a binomial setting and X has a binomial distribution with n = 10 and p = 0.10. No, this is not a binomial setting because the probability of success is not the same for each trial. No, this is not a binomial setting because the trials are not independent. No, this is not a binomial setting because there are not a fixed number of trials. No, this is not a binomial setting because the given scenario is not binary.A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. A survey of adults found that 61% have used a multivitamin in the past 12 months. You randomly select 50 adults and ask them if they have used a multivitamin in the past 12 months.To assess whether two data sets are derived from the same distribution—which need not be known, you can apply the test for _____________ that uses the chi-square distribution. The ________ hypothesis for this test states that the populations of the two data sets come from the same distribution. The test compares the observed values against the expected values if the two populations followed the same distribution. The test is right-tailed. Each observation or cell category must have an expected value of at least ______. Group of answer choices independence, null, four homogeneity, null, five goodness of fit, null, five variance test, alternate, four
- Both the Poisson and the binomial distributions are discrete distributions and both have a given number of trials. True FalseSampling and the Binomial Distribution. Refer to the discussion on the binomial approximation to the hypergeometric distribution. a. If sampling is with replacement, explain why the trials are independent and the success probability remains the same from trial to trial—always the proportion of the population that has the specified attribute. b. If sampling is without replacement, explain why the trials are not independent and the success probability varies from trial to trial.A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. A survey of adults found that 46% have used a multivitamin in the past 12 months You randomly select 50 adults and ask them past 12 months. they have used a multivitamin in the Select the correct answer below and, if necessary, fill in the answer boxes within your choice O A. No, because np <5. OB. No, because ng <5. O C. Yes, the mean is and the standard deviation is (Round to two decimal places as needed.)
- It is believed that 58% of Americans like to eat at restaurants every week. You interview 6 Americans and ask if they like to eat at restaurants every week. The random variable x represents the number of Americans that like to eat at restaurants every week. Find the mean of the binomial distribution. μ = ____________________________ Find the standard deviation of the binomial distribution. σ = __________________________ What is the probability that at least 1 of the Americans surveyed likes to eat at restaurants every week? Provide an answer to 4 decimal places.Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 40 and p = 0.18. (For each answer, enter a number. Use 2 decimal places.)n·p = n·q = Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____, p̂ _____ be approximated by a normal random variable because _____ _____.first blank YesNo second blank cancannot third blank n·q does not exceedboth n·p and n·q exceed n·p and n·q do not exceedn·p exceedsn·p does not exceedn·q exceeds fourth blank (Enter an exact number.)What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.)μp̂ = mu sub p hat = σp̂ = sigma sub p hat = (b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____,…Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 45 and p = 0.26. (For each answer, enter a number. Use 2 decimal places.)n·p = n·q = Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____, p̂ _____ be approximated by a normal random variable because _____ _____.first blank Yes No second blank can cannot third blank both n·p and n·q exceedn·q does not exceed n·p and n·q do not exceedn·q exceedsn·p does not exceedn·p exceeds fourth blank (Enter an exact number.)=What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.)μp̂ = σp̂ = (b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____, p̂ _____ be…
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