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Chapter 6 Test B Name: __________________________ Date: _____________ 1. Mrs. Smith's reading class can read a mean of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. What is the minimum number of words per minute a student would have to read in order to get the award? 2. The standard deviation of a distribution is 20. If a sample of 225 is selected, what is the standard error of the mean? 3. A survey of 250 lobster fishermen found that they catch an average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds? 4. What is the z value such that 50% of the total area lies to the right of the curve in any normal distribution? Page 1 Chapter 6 Test B 5. What is the z value such that 85% of the total area lies to the left of it, as shown in the figure below? 6. Find the probability P(z > 0.73) using the standard normal distribution. 7. If X is a normal random variable with mean 6 and standard deviation 3.0, then find the value x such that P(Z > x) is equal to .7054, as shown below. (Note: the diagram is not necessarily to scale.) 8. Find the probability P(Z < 0.22) using the standard normal distribution. Page 2 Chapter 6 Test B 9. For a normal curve with mean 8 and standard deviation 6, which of the following parts of the normal curve will have an area of approximately 34%? 10. If X is a normal random variable with standard deviation 3.50, and if the probability that X is more than 10.83 is .1271 (as shown below), then what is the mean of X? (Note: the diagram is not necessarily to scale.) 11. If X is a normal random variable with standard deviation 3.50, and if the probability that X is less than 8.83 is .648 (as shown below), then what is the mean of X? (Note: the diagram is not necessarily to scale.) 12. Find the probability P(–0.62 < z < –0.01) using the standard normal distribution. Page 3 Chapter 6 Test B 13. If X is a normal random variable with mean 4, and if the probability that X is less than 5.76 is .72 (as shown below), then what is the standard deviation of X? (Note: the diagram is not necessarily to scale.) 14. The mean weight of loads of rock is 43.0 tons with a standard deviation of 12.0 tons. If 9 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 38.60 tons. Assume that the variable is normally distributed. 15. Find the probability P(–1.04 < z < 1.11) using the standard normal distribution. 16. The average gas mileage of a certain model car is 26 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 1.3, find the probability that a car has a gas mileage of between 25.8 and 26.3 miles per gallon. Page 4 Chapter 6 Test B 17. The average length of crocodiles in a swamp is 12 feet. If the lengths are normally distributed with a standard deviation of 1.9, find the probability that a crocodile is more than 11.5 feet long. 18. On an easy test, the mean score was 97 out of a possible 100 points. The distribution of all test scores is mostly likely to be skewed in which way? 19. Find the probability P(0.26 < z < 1.33) using the standard normal distribution. 20. For a normal distribution with mean –9 and standard deviation 2, the value –10 has a z value of what? Page 5