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STA 2023 – Test #3 Practice Name _______________________ 1. In one region, the September energy consumption levels for single-family homes are bound to be normally distributed with a mean of 1,050 kWh and a standard deviation of 218 kWh. Find P45, which is the consumption level separating the bottom 45% from the top 55%. Round to the nearest tenth. 2. Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 3. The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz? Round your answer to four decimal places. 4. The lengths of pregnancies are normally distributed with a mean of 270 days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting 309 days or longer. b. If the length of pregnancy is in the lowest 4%, then the baby is premature. Find the length that separates premature babies from those who are not premature. 5. Determine whether the random variable is discrete or continuous. a. b. c. d. e. Is the number of free-throw attempts before the first shot is made discrete or continuous? Is the number of people in a restaurant that has a capacity of 150 discrete or continuous? Is the exact time it takes to evaluate 27 + 72 discrete or continuous? Is the square footage of a house discrete or continuous? Is the number of points scored during a basketball game discrete or continuous? 6. A TV show, Lindsay and Tobias, recently had a share of 25, meaning that among the TV sets in use, 25% were tuned to that show. Assume that an advertiser wants to verify that 25% share value by conducting its own survey, and a pilot survey begins with 16 households having TV sets in use at the time of a Lindsay and Tobias broadcast. a. b. c. d. Find the probability that none of the households are tuned to Lindsay and Tobias. Find the probability that at least one household is tuned to Lindsay and Tobias. Find the probability that at most one household is tuned to Lindsay and Tobias. If at most one household is tuned to Lindsay and Tobias, does it appear that the 25% share value is wrong? Why or why not? 7. Assume that the readings on the thermometers are normally distributed with a mean of 0 and a standard deviation of 1.00C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to P83, the 83rd percentile. This is the temperature reading separating the bottom 83% from the top 17%. STA 2023 – Test #3 Practice Name _______________________ 8. If z is a standard normal variable, find the probability. Round your answer to four decimal places. P(z>0.59) 9. A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? Round to three decimal places. 10. A brand name has a 60% recognition rate. If the owner of the brand wants to verify that rate by beginning with a small sample of 10 randomly selected consumers, find the probability that exactly 6 of the 10 consumers recognize the brand name. Also find the probability that the number who recognized the brand name is not 6. 11. Assume that the readings on the thermometers are normally distributed with a mean of 0 and a standard deviation of 1.00C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in Celsius degrees.) Between 1.50 and 2.25 12. Assume that X has a normal distribution. The mean is =60.0 and the standard deviation is =4.0. Find the probability that X is less than 53.0. 13. Find the mean of the given probability distribution. The random variable x is the number of houses sold by a realtor in a single month at the Sendsom’s Real Estate office. Houses Sold (x) 0 1 2 3 4 5 6 7 Probability P(x) 0.24 0.01 0.12 0.16 0.01 0.14 0.11 0.21 14. Suppose that 14% of people are left handed. If 6 people are selected at random, what is the probability that exactly 2 of them are left handed? Round to three decimal places. 15. An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 181 lb. The new population of pilots has normally distributed weights with a mean of 149 lb and a standard deviation of 29.5 lb. a. If a pilot is randomly selected, find the probability that his weight is between 140 lb and 181 lb. b. If 31 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 181 lb. c. When redesigning the ejection seat, which probability is more relevant? 16. Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than - 2 or greater than + 2. STA 2023 – Test #3 Practice Name _______________________ A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 576 consumers who recognize the Dull Computer Company name? 17. Based on a survey, for women aged 18 to 24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.9 and a standard deviation of 13.1. Complete parts (a) through (d). a. If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is greater than 110. b. If 3 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 110. c. Given that part (b) involves a sample size that is not larger than 30, why can the central limit theorem be used? a) When the original population is normally distributed, the central limit theorem can only be used if the sample size is less than or equal to 30. b) Since the original population is normally distributed, the sampling distribution of sample means will be normally distributed for any sample size. c) The central limit theorem can always be used regardless of sample size. d) Since the 3 women are randomly selected, the sampling distribution of sample means will be normally distributed for any sample size. d. If a physician is given a report stating that 3 women have a mean systolic blood pressure below 110, can she conclude that none of the women have a blood pressure greater than 110? Why? 18. In a certain town, 60% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree. Find the standard deviation for the probability distribution. Round to the nearest hundredth. x 0 1 2 3 4 P(x) 0.0256 0.1536 0.3456 0.3456 0.1296 19. A car insurance company has determined that 6% of all drivers were involved in a car accident last year. Among the 13 drivers living on one particular street, 3 were involved in a car accident last year. If 13 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year? Round to three decimal places. 20. Using the following uniform density curve, answer the question. What is the probability that the random variable has a value greater than 5? Round to three decimal places. 21. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. n=6, x=3, p=0.45 STA 2023 – Test #3 Practice Name _______________________ 22. A candy company claims that 24% of its plain candies are orange, and a sample of 200 such candies is randomly selected. a. Find the mean and standard deviation for the number of orange candies in such groups of 200. b. A random sample of 200 candies contains 50 orange candies. Is this result unusual? Does it seem that the claimed rate of 24% is wrong? 23. Assume the readings on thermometers are normally distributed with a mean of 0C and a standard deviation of 1.00C. Find the probability that a randomly selected thermometer reads greater than -2.24C and draw a sketch of the region. 24. Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 25. The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 106 inches, and a standard deviation of 12 inches. What is the probability that the mean annual snowfall during 36 randomly picked years will exceed 108.8 inches? Round your answer to four decimal places.