Find the area of the indicated region under the standard normal curve. Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. ,o,9 E The area between 2 = - 1.3 and 2: 1.5 under the standard normal curve is (Round to four decimal places as needed.) Find the indicated probability using the standard normal distribution. P(z > 1.87) Click here to View [age 1 of the standard normal table. Click here to View [ge 2 of the standard normal table. <:> P(z> 1.87) = Cl (Round to four decimal places as needed.) Assume the random variable x is normally distributed with mean u = 50 and standard deviation 6 = 7. Find the indicated probability. P(x>41) E> P(x>41)=|:| (Round to four decimal places as needed.) In a survey of a group of men, the heights in the 2029 age group were normally distributed, with a mean of 69.7 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than 67 inches tail is . (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 67 and 72 inches. The probability that the study participant selected at random is between 67 and 72 inches tail is . (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 72 inches. The probability that the study participant selected at random is more than 72 inches tail is . (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. There are no unusual events because all the probabilities are greater than 0.05. The event in part (a) is unusual because its probability is less than 0.05. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05. .5997? The events in parts (a) and (c) are unusual because its probabilities are less than 0.05. Find the indicated z-score shown in the graph to the right. Area = 0 '3085 The z-score is . (Round to two decimal places as needed.) The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution, as shown in the gure. (a) What is the minimum UGPAthat would still place a student in the top 15% of UGPAs? 3 32 (b) Between what two values does the middle 50% of the UGPAs lie? P ' 0' 0.1 2.64 3.32 4 Grade point average 9,6 (a) The minimum UGPAthat would still place a student in the top 15% of UGPAs is (Round to two decimal places as needed.) (b) The middle 50% of UGPAs lies between on the low end and on the high end. (Round to two decimal places as needed.) The graph of the waiting time (in seconds) at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of 225 is drawn from the population. Decide which of the graphs labeled (a)(c) would most closely resemble the sampling distribution of the sample means. Explain your reasoning. (b) (C) i a a 0-04 (5.)=12.ea' a S S X S g , 2' 4o 40 D Time (in sec.) Time (in sec.) Time (in sec.) Time (in sec.) Graph V most closely resembles the sampling distribution of the sample means, because [1; = , a; = , and the graph V . is the same shape as the graph for the original distribution approximates a normal curve