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Exam 4 preparation Math 12 7.2, 7.3, 8.1 7.2 The Standard Normal Distribution Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Find the area under the standard normal curve between z = 0 and z = 3. A) 0.4987 B) 0.9987 C) 0.0010 D) 0.4641 2) Find the area under the standard normal curve between z = -1.5 and z = 2.5. A) 0.9270 B) 0.7182 C) 0.6312 D) 0.9831 3) Find the area under the standard normal curve to the right of z = -1.25. A) 0.8944 B) 0.5843 C) 0.6978 D) 0.7193 4) Find the area under the standard normal curve to the left of z = 1.25. A) 0.8944 B) 0.1056 C) 0.2318 D) 0.7682 5) Find the area under the standard normal curve between z = 1.5 and z = 2.5. A) 0.0606 B) 0.9938 C) 0.9332 D) 0.9816 6) Find the area under the standard normal curve between z = -1.25 and z = 1.25. A) 0.7888 B) 0.8817 C) 0.6412 D) 0.2112 7) Given a distribution that follows a standard normal curve, what does the graph of the curve do as z increases in the positive direction? A) The graph of the curve approaches zero. B) The graph of the curve approaches 1. C) The graph of the curve approaches an inflection point. D) The graph of the curve eventually intersects the horizontal axis. 8) For a standard normal curve, find the z-score that separates the bottom 30% from the top 70%. A) -0.53 B) -0.98 C) -0.47 D) -0.12 1 9) For a standard normal curve, find the z-score that separates the bottom 70% from the top 30%. A) 0.53 B) 0.98 C) 0.47 D) 0.12 10) Find the z-scores for which 98% of the distribution’s area lies between -z and z. A) (-2.33, 2.33) B) (-1.645, 1.645) C) (-1.96, 1.96) D) (-0.99, 0.99) 11) Find the z-score that is less than the mean and for which 70% of the distribution’s area lies to its right. A) -0.53 B) -0.98 C) -0.81 D) -0.47 12) Scores on a standardized test are normally distributed with a mean of 104 and a standard deviation of 20. An Individual’s test score is found to be 109. Find the z-score corresponding to this value. A) 0.25 B) -0.25 C) 4.00 D) -4.00 13) Use the standard normal distribution to find P(0 < Z < 2.25). A) 0.4878 B) 0.5122 C) 0.8817 D) 0.7888 14) Use the standard normal distribution to find P(-2.50 < Z < 1.50). A) 0.9270 B) 0.8822 C) 0.6167 D) 0.5496 15) Determine the area under the standard normal curve that lies between: z = 1 and z = 2 A) 0.1359 B) 0.8641 C) 0.0006 D) 0.0008 16) Determine the area under the standard normal curve that lies between: z = 0.5 and z = 1.4 A) 0.2277 B) 0.6915 C) 0.9192 D) 0.3085 7.3 Applications of the Normal Distribution 17) Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Find the percentage of buyers who paid: between $148,200 and $151,800 if the standard deviation is $1800. A) 68% B) 34% C) 95% D) 99.7% 2 18) Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Find the percentage of buyers who paid: between $150,000 and $156,300 if the standard deviation is $2100. A) 49.85% B) 99.7% C) 34% D) 47.5% 19) Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Find the percentage of buyers who paid: more than $153,800 if the standard deviation is $1900. A) 2.5% B) 97.5% C) 47.5% D) 95% 20) Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Find the percentage of buyers who paid: less than $146,600 if the standard deviation is $1700. A) 2.5% B) 97.5% C) 47.5% D) 95% 21) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 322 seconds. A) 0.0107 B) 0.4893 C) 0.9893 D) 0.5107 22) Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 11.14 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains more than 11.14 ounces of beer. A) 0.5 B) 1 C) 0 D) 0.4 23) Use the standard normal distribution to find P(-2.25 < z < 0). A) 0.4878 B) 0.5122 C) 0.6831 D) 0.0122 A) Use the standard normal distribution to find P(-2.25 < z < 1.25). A) 0.8822 B) 0.0122 C) 0.4878 D) 0.8944 24) Suppose a brewery has a filling machine that fills 12-ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.15 ounces and a standard deviation of 0.04 ounce. The company is interested in reducing the amount of extra beer that is poured into the 12 ounce bottles. The company is seeking to identify the highest 1.5% of the fill amounts poured by this machine. For what fill amount are they searching? A) 12.237 oz B) 11.913 oz C) 12.063 oz D) 12.087 oz 3 25) The mean incubation time for a type of fertilized egg kept at 100.7ºF is 21 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day. a)What is the probability that randomly selected fertilized egg hatches in less than 19 days? b)What is the probability that randomly selected fertilized egg takes over 23 days to hatch? c)What is the probability that randomly selected fertilized egg hatches between 20 and 21 days? d)Would it unusual for an egg to hatch in less than 18 days? Answer: a) 0.0228 , b) 0.0228 , c) 0.3413 , d) Unusual, P(event) = 0.0013 8.1 Distribution of the Sample Mean 26) According to the law of large numbers, as more observations are added to the sample, the difference between the sample mean and the population mean A) Tends to become smaller B) Tends to become larger C) Remains about the same D) Is inversely affected by the data added 27) Suppose a population has a mean of 7 for some characteristic of interest and a standard deviation of 9.6. A sample is drawn from this population of size 64. What is the standard error of the mean? A) 1.2 B) 0.7 C) 0.15 D) 3.3 use x n 12) Furnace repair bills are normally distributed with a mean of 271 dollars and a standard deviation of 15 dollars. If 36 of these repair bills are randomly selected, find the probability that they have a mean cost between 271 dollars and 273 dollars. A) 0.2881 B) 0.7881 C) 0.2119 D) 0.5517 13) Assume that the heights of men are normally distributed with a mean of 67.9 inches and a standard deviation of 2.1 inches. If 36 men are randomly selected, find the probability that they have a mean height greater than 68.9 inches. A) 0.0021 B) 0.0210 C) 0.9005 D) 0.9979 5) The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standard deviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability that the mean daily revenue for the next 30 days will exceed $7000? A) 0.1814 B) 0.8186 C) 0.5675 D) 0.4325 4