Question: 1. 4.1 problem 2 Think about a density curve that consist of two straight-line segments. The first goes from the point (0, 1) to the

1. 4.1 problem 2 Think about a density curve that consist of two straight-line segments. The first goes from the point (0, 1) to the point (0.7, 1) then the second goes from the point (0.7, 1) to the point (1.3, 0) a) sketch the density curve b) what is the probability that X falls below 0.5? c) what is the probability that X lies between 0.7 and 1.3? d) what is the probability that X lies above 0.2 e) what is the probability that X is equal to 0.5? 2. 4.2 problem 4 The heights of American women aged 18 to 24 are approximately normally distributed with mean 65 inches and standard deviation 2.1 inches. Half of all young women are shorter than what weight? 3. 4.2 problem 6 The length of time needed to complete a certain test is normally distributed with mean 57 minutes and standard deviation 8 minutes. a) what is the relative frequency of people who take between 49 and 65 minutes to complete the test? Sketch the distribution and shade in the area in question. b) find the interval that contains the middle 95% of completion times for all people taking the test. 4. 4.3 problem 6 A calculus exam had a mean of 75 and a standard deviation of 6. If Sally had made a 78 on this exam, what is her z-score? 5. 4.3 problem 12 The heights of American men aged 18 to 24 are approximately normally distributed with mean 68 inches and standard deviation 2.5 inches. Only about 5% of young men have heights above what height? 6. 4.3 problem 16 Find the following probabilities: a. P(Z<1.82) b. P(1.680.56) d. P(0.52 < Z < 0.52) e. P(2.091.08) 7. 4.3 problem 18 Find the value of c that satisfies each of the following probabilities: a. P(Z < c)= 0.0495 b. P(Z < c)= 0.8438 c. P(Z > c)= 0.0778 d. P(c < Z < c)= 0.9774 8. 4.3 problem 20 Suppose X is a normal distribution with N(210, 32). Find the following: a. b. c. d. e. P(X<230) P(180190) Find c such that P(X < c)= 0.0344 Find c such that P(X > c)= 0.7486

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