Exam 5: A Normal World

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?

Which of the following statements concerning areas under the standard normal curve is/are true? a) If a z-score is negative, the area to its right is greater than 0.5 b) If the area to the right of a z-score is less than 0.5, the z-score is negative. c) If a z-score is positive, the area to its left is less than 0.5

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?

Decide which of the described variables is/are likely have a normal or near-normal distribution. a. The heights of corn stalks in one row of corn that is half a mile long b.The numbers of viewers of each of the channels from 202 to 550 on Direct TV at 7:00 PM CDT on the third Thursday of November 2012 (349 data values)

The amount of Jen's monthly electric bill is normally distributed with a mean of $160 and a standard deviation of $14. Fill in the blanks. 95% of her electric bills are between $_____ and $_____.

Which of the following statements concerning the standard normal curve is/are true (if any)? a) The area under the standard normal curve to the left of −3 is zero. b) The area under the standard normal curve between any two z-scores is greater than zero. c) The area under the standard normal curve between two z-scores will be negative if both Z-scores are negative. d) The area under the standard normal curve to the left of any z-score is less than 1.

Apply the 68-95-99.7 rule to answer -The annual precipitation for one city is normally distributed with a mean of 28 inches and a standard deviation of 3.4 inches. Fill in the blanks. in 95% of the years, the precipitation in this city is between _____ and _____ inches.

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.)

Select the distribution that appears to be the most normal.

The area under the standard normal curve between 1 and 2 is equal to 0.1359. Scores on a particular aptitude test are normally distributed with a mean of 100 and a standard deviation of 10. Which of the following are equal to 13.59%? a. The percentage of scores between 120 and 130 b. The percentage of scores between 110 and 120 c. The percentage of scores between 80 and 90 d. The percentage of scores between 90 and 120 e. The percentage of scores between 90 and 110

The mean score on the exit examination for an urban high school is 63 with a standard deviation of 9. What is the standard deviation of the distribution of sample means with a sample size of 9?

Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Find the 60th percentile.

Apply the 68-95-99.7 rule to answer -The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mm Hg and a standard deviation of 12 mm Hg. What percentage of 18-year-old women have a systolic blood pressure that is within 3 standard deviations of the mean on either side?

Many colleges require SAT scores of high school students for admission. The scores on each part of the test range from 200 to 800. In one year, the mean verbal score was 431 with a standard deviation of 119, while the mean mathematical score was 472 with a standard deviation of 128. Find the percentile for a verbal score of 550. Then find the score on the mathematics portion of the test that has the same percentile.

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 270 hours and a standard deviation of 11 hours. What percentage of the bulbs have lifetimes that lie within 2 standard deviations of the mean on either side?

Which set of data represented by the three histograms below most likely came from a normal distribution?

The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 6. If 9 fish are randomly selected, what is the likelihood that the mean weight will be between 17.6 and 21.6 lb?

The mean life of a set of AAA batteries used in a handheld GPS (Global Positioning System) unit is 8 hours with a standard deviation of 0.5 hours. Assuming that the battery lives are normally distributed, if a class uses 16 of these units on a field trip, approximately how many will still be working after 8.25 hours?

The scores on a certain test are normally distributed with a mean score of 58 and a standard deviation of 4. What is the likelihood that a sample of 90 students will have a mean score of at least 58.4216?

The weights of a large population of male students have a mean of 160 pounds with a standard deviation of 15 pounds. What is the mean of the distribution of sample means for samples of 16 students?