A population of values has a normal distribution with p. = 126.5 and 0' = 73. You intend to draw a random sample of size n = 181. {a} Find the probability that a single randomly selected value is greater than 139.5. {b} Find the probability that a sample of size n = 181 is randomly selected with a mean greater than 139.5. P(:E >139.5}=:] Enter your answers as numbers rounded to 4 places after the decimal point, if necessary. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. A population of values has a normal distribution with ,u = 52.8 and cr = 13.1. You intend to draw a random sample of size n, = 58. What is the mean of the distribution of sample means? #f C] (Round your answer to 2 places after the decimal point, if necessary.) What is the standard deviation of the distribution of sample means? C] (Round your answer to 2 places after the decimal point, if necessary.) 05 The arrows can only be dragged to z scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis). So round all z scores to 1 decimal place, if necessary. (a) Sketch the region corresponding to the statement P(z c) = 0.2. Shade: Left of a value v . Click and drag the arrows to adjust the values. -4 -3 -2 -1 0 2 3 -1.5Suppose that the heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.61 inches. Suppose further that the heights of adult women in America are also normally distributed, but with a mean of 64.1 inches and a standard deviation of 2.55 inches. a) If a man is 6-feet 3-inches tall, what is his 2 score? (Round your answer to 2 places after the decimal point, if necessary.) z.[ b} What percentage of men are SHORTER than 6-feet-3 inches? (Round your answer to the nearest tenth of a percent--1 place after the decimal point--if necessary. Do NOT type a \"%" symbol after your answer.) g]% c) If a woman is 5-feet 11-inches tall, what is her 2 score? [Round your answer to 2 places after the decimal point, if necessary.) z.[ d} What percentage of women are TALLER than 5-feet 11-inches? (Round your answer to the nearest tenth of a percent--1 place after the decimal point--if necessary. Do NOT type a "953" symbol after your answer.) g]% e) Who is relatively taller: a 6'3" American man or a 5'1 1" American woman? Defend your choice in a meaningful sentence