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ProbStat PRACTICE TEST 6.1-6.2 Name___________________________________ 1) Find the area under the standard normal curve to the left of z = 2.6. 1) 2) Find the area under the standard normal curve to the right of z = -2.2. 2) 3) Find the area under the standard normal curve that lies between z = -2.8 and z = -2.2. 3) 4) The average height of flowering cherry trees in a certain nursery is 10.5 feet. If the heights are normally distributed with a standard deviation of 1.5 feet, find the probability that a tree is less than 12.5 feet tall. 4) 5) A normal population has a mean µ = 24 and standard deviation σ = 5. What is the probability that a randomly chosen value will be greater than 26? 5) 6) The average gas mileage of a certain model car is 26.0 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 0.15 miles per gallon, find the probability that a car has a gas mileage of between 25.8 and 26.2 miles per gallon. 6) 7) Find the probability P(z < 0.32) using the standard normal distribution. 7) 8) Find the probability P(z > -0.74) using the standard normal distribution. 8) 9) Find the probability P(-0.94 < z < 1.21) using the standard normal distribution. 9) 10) Find the z-score for which the area to the left is 0.14. 10) 11) Find the z-score for which the area to the right is 0.77. 11) 12) Find the z-scores that bound the middle 92% of the area under the standard normal curve. 12) 13) X is a normally distributed random variable with a standard deviation of 3.00. Find the mean of X when 64.8% of the area lies to the left of 9.14. 13) 1 14) X is a normally distributed random variable with a mean of 5 and a standard deviation of 2.0. Find the value of X for which 70.54% of the area under the distribution curve lies to the right of it. 14) 15) X is a normally distributed random variable with a mean of 11.0. If 59.10% of the data lies to the right of 10.43 find the standard deviation. 15) 2 Answer Key Testname: PROBSTAT PRACTICE TEST 6.1-6.2 1) 0.9953 2) 0.9861 3) 0.0113 4) 0.91 5) 0.3446 6) 0.816 7) 0.6255 8) 0.7704 9) 0.7133 10) -1.08 11) -0.74 12) -1.75, 1.75 13) 8.0 14) 3.92 15) 2.5 3