<p>Name______Date ______</p><p>Introduction to Probability & Statistics Ch.5 Review</p><p>1. If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, use the 68-95-99.7 rule to approximate the percentage of light bulbs having a life between 2000 hours and 3500 hours?</p><p>2. The average height of women is 65 inches with a standard deviation of 3 inches. What percentile does Jane fall in if she is 5’1”? And what does this suggest?</p><p>3. The mean annual mileage of cars for a rental car fleet is 12,000 miles with a standard deviation of 2,415 miles. If 225 cars were sampled what is the chance that the mean of the distribution of sample means is less than 10,000 miles?</p><p>4. The mean life of light bulbs is 2500 hours with a standard deviation of 500 hours. If 300 bulbs were tested individually, approximately how many would have a lifetime between 2000 and 3000 hours?</p><p>5. Determine whether each statement is true or false. a. A z-score of 1.75 is considered unusual.</p><p> b. The standard deviation of a sample gets bigger as the sample size increases.</p><p> c. The area under the normal curve is 100%</p><p> d. The weight of all males in the U.S. would be best described as normal e. The area to the left of the mean is negative. 6. Assuming the weights for a sample of cats are normally distributed with a mean of 11 pounds and a standard deviation of 2 pounds, find the following quantities using the 68-95-99.7 Rule. a. Percentage of cats weighing less than 9 pounds. </p><p> b. Percentage of cats weighing more than 15 pounds.</p><p> c. Percentage of cats weighing between 13 and 15 pounds. </p><p> d. Percentage of cats weighing between 7 and 13 pounds.</p><p>7. The amount of Jen’s monthly phone bill is normally distributed with a mean of $60 and a standard deviation of $12. Fill in the blanks.</p><p>95% of her phone bills are between $______and $______. 8. The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during 25 randomly picked years will be less than 90.8 inches?</p><p>9. Assume that women have heights that are normally distributed with a mean of 65 inches and a standard deviation of 3 inches. Find the height that corresponds to the 93rd percentile.</p><p>10. The mean score on the exit examination for an urban high school is 63 with a standard deviation of 8. What is the mean of the distribution of sample means with a sample size of 9?</p><p>11. The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. In a random sample of 1500 bolts tested, how many will have a diameter greater than 0.32 inches? 12. A math teacher gives two different tests to measure students’ aptitude for math. Scores on the first test are normally distributed with a mean of 24 and a standard deviation of 4.5. Scores on the second test are normally distributed with a mean of 70 and a standard deviation of 11.3. Assume that the two tests use different scales to measure the same aptitude. If a student scores 29 on the first test, what would be his equivalent score on the second test? (That is, find the score that would put him in the same percentile.)</p><p>13. 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 190 and 230. </p><p>14. A rocket club makes its own rockets. The rockets go to a mean height of 1100 feet with a standard deviation of 60 feet. If the club fires 100 rockets, what is probability that the mean height of the rockets will be between 1020 and 1150 feet?</p>