CH 6 Review Normal Probability Distributions College Statistics

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1 CH 6 Review Normal Probability Distributions College Statistics Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Using the following uniform density curve, answer the question. 1) What is the probability that the random variable has a value greater than 5? 1) A) B) C) D) ) What is the probability that the random variable has a value between 0.4 and 0.8? 2) A) 0.3 B) 0.05 C) D) Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 3) 3) A) B) C) D) ) 4) A) B) C) D) Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 5) Shaded area is ) A) 1.45 B) 1.26 C) 1.39 D)

2 6) Shaded area is ) A) 0.25 B) 0.57 C) D) If z is a standard normal variable, find the probability. 7) The probability that z lies between 0 and ) A) B) C) D) ) The probability that z lies between 0.7 and ) A) B) C) D) ) The probability that z is greater than ) A) B) C) D) Solve the problem. 10) For a standard normal distribution, find the percentage of data that are more than 2 standard deviations below the mean or more than 3 standard deviations above the mean. A) 97.59% B) 2.41% C) 0.26% D) 4.56% 10) Solve the problem. Round to the nearest tenth unless indicated otherwise. 11) In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kwh and a standard deviation of 218 kwh. Find P45, which is the consumption level separating the bottom 45% from the top 55%. A) B) C) D) ) 12) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. Find P60, the score which separates the lower 60% from the top 40%. A) B) C) D) ) 2

3 Assume that X has a normal distribution, and find the indicated probability. 13) The mean is µ= 15.2 and the standard deviation is = 0.9. Find the probability that X is greater than A) B) C) D) ) 14) The mean is µ = 60.0 and the standard deviation is = 4.0. Find the probability that X is less than A) B) C) D) ) Find the indicated probability. 15) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 170 and 220. A) B) C) D) ) Solve the problem. 16) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches, and a standard deviation of 10 inches. What is the probability that the mean annual snowfall during 25 randomly picked years will exceed 72.8 inches? A) B) C) D) ) 17) The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 9. If 9 fish are randomly selected, what is the probability that the mean weight will be between 17.6 and 23.6 lb? A) B) C) D) ) 3

4 18) Human body temperatures are normally distributed with a mean of F and a standard deviation of 0.62 F. If 19 people are randomly selected, find the probability that their mean body temperature will be less than F. A) B) C) D) ) The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. 19) The probability of more than 44 correct answers 19) A) The area to the left of 44.5 B) The area to the right of 44.5 C) The area to the right of 44 D) The area to the right of ) The probability of fewer than 43 democrats 20) A) The area to the left of 43 B) The area to the left of 42.5 C) The area to the right of 43.5 D) The area to the left of ) The probability of no more than 35 defective CD's 21) A) The area to the right of 35.5 B) The area to the left of 35 C) The area to the left of 35.5 D) The area to the left of

5 Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. 22) A certain question on a test is answered correctly by 22% of the respondents. Estimate the 22) probability that among the next 150 responses there will be at most 40 correct answers. A) B) C) D) ) In one county, the conviction rate for speeding is 85%. Estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions. A) B) C) D) ) Use the normal distribution to approximate the desired probability. 24) Find the probability that in 200 tosses of a fair die, we will obtain at least 30 fives. 24) A) B) C) D)

6 Answer Key Testname: CH 6 REVIEW 1) A 2) B 3) B 4) A 5) D 6) D 7) B 8) A 9) C 10) B 11) D 12) D 13) B 14) D 15) C 16) D 17) C 18) D 19) B 20) B 21) C 22) A 23) A 24) A 6