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In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. It is known that 77% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 66 new products, find the following probabilities. (Round your answers to four decimal places.) A USE SALT (a) within 2 years 47 or more fail 0.862 (b) within 2 years 58 or fewer fail 0.982 (c) within 2 years 15 or more succeed X 0.521 (d) within 2 years fewer than 10 succeed X 0.068
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. It is estimated that 3.4% of the general population will live past their 90th birthday. In a graduating class of 796 high school seniors, find the following probabilities. (Round your answers to four decimal places.) A USE SALT (a) 15 or more will live beyond their 90th birthday (b) 30 or more will live beyond their goth birthday (c) between 25 and 35 will live beyond their goth birthday (d) more than 40 will live beyond their 90th birthday
Suppose x has a distribution with x = 24 and a = 22. USE SALT (a) If a random sample of size n = 50 is drawn, find and P(24 sX s 26). (Round or to two decimal places and the probability to four decimal places.) M[24 7- 1.21 X P(24 SX s 26) = (b) If a random sample of size n = 69 is drawn, find go and P(24 sX s 26). (Round to two decimal places and the probability to four decimal places.) 24 P(24 S * S 26) = (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is smaller than part (ə) because of the larger sample size. Therefore, the distribution about is narrower
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard deviation 6 inches. in USE SALT (a) What is the probability that an 18-year-old man selected at random is between 68 and 70 inches tall? (Round your answer to four decimal places.) 0.1350 (b) If a random sample of thirteen 18-year-old men is selected, what is the probability that the mean height * is betw 68 and 70 inches? (Round your answer to four decimal places.) 0.5762 X etween (c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this? The probability in part (b) is much higher because the mean is smaller for the x distribution The probability in part (b) is much higher because the standard deviation is larger for the x distribution. The probability in part (b) is much higher because the standard deviation is smaller for the distribution. The probability in part (b) is much higher because the mean is larger for the distribution The probability in part (b) is much lower because the standard deviation is smaller for the x distribution OOOO Need Help? Road Watch
Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, has a distribution that is approximately normal, with mean = 73 and estimated standard deviation o = 46. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed. USE SALT (a) What is the probability that, on a single test, * < 40? (Round your answer to four decimal places.) (b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of ? Hint: See Theorem 6.1. The probability distribution of x is not normal. The probability distribution of x is approximately normal with #x - 73 and 46. The probability distribution of is approximately normal with 2 - 73 and The probability distribution of x is approximately normal with = 73 and 7 = 23.00. - 32.53 What is the probability that * < 40? (Round your answer to four decimal places.) (C) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.) (c) Compare your answers to parts (a), (b), (c), and (d). Did the probabilitles decrease as n increased? Yes No Explain what this might imply if you were a doctor or a nurse. The more tests a patient completes, the stronger is the evidence for excess insulin The more tests a patient completes, the weaker is the evidence for lack of insulin The more tests a patient completes, the stronger is the evidence for lack of insulin. The more tests a patient completes, the weaker is the evidence for excess insulin
Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean y = 6850 and estimated standard deviation o = 2250. A test result of * < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection. USE SALT (a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.) (b) Suppose a doctor uses the average for two tests taken about a week apart. What can we say about the probability distribution of ? The probability distribution of x is not normal. The probability distribution of x is approximately normal with My = 5850 and 5 = 1125.00 The probability distribution of x is approximately normal with = 6850 and o- 1590.99. The probability distribution of x is approximately normal with = 6850 and 7-2250. What is the probability of x < 3500? (Round your answer to four decimal places.) (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) (d) Compare your answers to parts (a), (b), and (C). How did the probabilities change as n increased? The probabilities decreased as n increased. The probabilities increased as n increased. The probabilities stayed the same as n increased. OO If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse? It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia. It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia. O it would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia. It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.
A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 400 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean # - 1.3% and standard deviation - 0.9%. in USE SALT (a) Let's consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks. Is it reasonable to assume that x (the average monthly return on the 400 stocks in the fund) has a distribution that is approximately normal? Explain. Yes x is a mean of a sample of n = 400 stocks. By the central limit theorem the x distribution is approximately normal. (b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.) (c) After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.) (d) Compare your answers to parts (b) and (c). Did the probability increase as n (number of months) increased? Why would this happen? Yes, probability increases as the standard deviation increases. Yes, probability increases as the mean increases, No, the probability stayed the same. Yes, probability increases as the standard deviation decreases. (e) If after 18 months the average monthly percentage return x is more than 2%, would that tend to shake your confidence in the statement that w = 1.3%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.) P(x > 2%) Explain. This is very likely if u = 1.3%. One would suspect that the European stock market may be heating up. This is very likely if = 1.3%. One would not suspect that the European stock market may be heating up. This is very unlikely if # = 1.3%. One would not suspect that the European stock market may be heating up. This is very unlikely if = 1.3%. One would suspect that the European stock market may be heating up.
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. It is known that 77% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 66 new products, find the following probabilities. (Round your answers to four decimal places.) A USE SALT (a) within 2 years 47 or more fail 0.862 (b) within 2 years 58 or fewer fail 0.982 (c) within 2 years 15 or more succeed X 0.521 (d) within 2 years fewer than 10 succeed X 0.068