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Assume that females have pulse rates that are normally distributed with a mean of u = 74.0 beats per minute and a standard deviation of o = 12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 80 beats per minute. The probability is 0.6844 . (Round to four decimal places as needed.) b. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 80 beats per minute. The probability is (Round to four decimal places as needed.)2. A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 193 lb and a standard deviation of 35 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3750 lb. Complete parts (a) through (d) below. (Type an integer or a decimal. Do not round.) b. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)? The probability is 1.0000 . (Round to four decimal places as needed.) c. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 187.5 lb, which is the maximum mean weight that does not cause the total load to exceed 3750 lb? The probability is (Round to four decimal places as needed.)3. Suppose that an airline uses a seat width of 16.9 in. Assume men have hip breadths that are normally distributed with a mean of 14.7 in. and a standard deviation of 1 in. Complete parts (a) through (c) below. (a) Find the probability that if an individual man is randomly selected, his hip breadth will be greater than 16.9 in. The probability is 0.0139 . (Round to four decimal places as needed.) (b) If a plane is filled with 128 randomly selected men, find the probability that these men have a mean hip breadth greater than 16.9 in. The probability is (Round to four decimal places as needed.)4. A sample of human brain volumes (cm) is given below. Use the given data values to identify the corresponding z scores that are used for a normal quantile plot, then identify the coordinates of each point in the normal quantile plot. Construct the normal quantile plot, then determine whether the data appear to be from a population with a normal distribution. 1022 1421 1082 1053 1072 1082 955 1063 List the z scores for the normal quantile plot. .0.0.0.0.0. 0.0 (Round to two decimal places as needed. Use ascending order.)5. Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 178 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. Probability that fewer than 44 voted The probability that fewer than 44 of 178 eligible voters voted is (Round to four decimal places as needed.)6. When a scientist conducted a genetics experiments with peas, one sample of offspring consisted of 947 peas, with 743 of them having red flowers. If we assume, as the scientist did, that under these circumstances, there is a 3 /4 probability that a pea will have a red flower, we would expect that 710.25 (or about 710) of the peas would have red flowers, so the result of 743 peas with red flowers is more than expected. a. If the scientist's assumed probability is correct, find the probability of getting 743 or more peas with red flowers. b. Is 743 peas with red flowers significantly high? c. What do these results suggest about the scientist's assumption that 3/ 4 of peas will have red flowers? a. If the scientist's assumed probability is correct, the probability of getting 743 or more peas with red flowers is (Round to four decimal places as needed.)
