• 1.The diameters of the trees in a stand of 100-year old Ponderosa Pines are normally distributed with a mean of 15 inches and a standard deviation of 4 inches.If only trees with diameters of 8 inches or more are marketable, what proportion of the stand is marketable?

• 2.
  • a. Over the years, the scores on the final exam in General Psychology have been normally distributed with a mean of 75 and a standard deviation of 8. What proportion would be expected to score between 70 and 85?
  • b. For the problem above, what scores separate the upper 1/2% and the lower 1/2% from the rest of the population?

   

• 3. A common technique in the field of testing is to arrange scores so that a test will have a mean of 50 and a standard deviation of 10. For such a test,
  • a. what scores separate the middle 25% from the rest?
  • b. what proportion would be expected to score 68 and above?
  • c. what proportion would be expected to score between 45 and 55?
  • d. what proportion would be expected to score between 55 and 65?
  • e. what proportion score above 35?
  • f. what score separates the top third on such a test?

   

• 4. From a normal distribution with a mean of 150 and a standard deviation of 50, find
  • a. the proportion of scores less than 225.
  • b. the proportion of scores less than 0.
  • c. the number of scores of 175 or more in a population of 500 scores.

• 5. For a normal distribution with a mean of 32 and a standard deviation of 3,
  • a. find the proportion of the distribution scoring 30 or more.
  • b. find the proportion that scored between 30 and 35.
  • c. find the scores that separate the middle 60% from the extremes.

   

• 6. On the average it takes 27 throws to complete the College Frisbee Golf Course. The standard deviation about this mean is 4.
  • a. What proportion of the population would be expected to score 22 or less (par)?
  • b. What proportion would score between 25 and 30? .
  • c. If 950 students played and a prize was given for scoring 20 or less, how many would get prizes?
  • d. Suppose an experimenter wanted to find some very good and some
  • very poor frisbee players to use in an experiment. She decided to use
  • the top 10 percent and the bottom 10 percent from the CFGC. What
  • are the cutoff scores?
  • e. What proportion would be expected to score between 28 and 32?
  • f. What assumption is being made about the nature of the distribution of frisbee golf scores in the questions above?

   

• 7.
  • a. Suppose you drew a random sample of 100 from a population and found X =30, s = 1. What is the probability that the sample was drawn from a population in which M = 29.75?
  • b. Set 95% confidence limits a out the sample mean.

   

• 8. Establish a 99% confidence interval about X= 31, given that s = 5, and N = 56. Write a sentence that explains the confidence interval that you have established.

• 9. What is the probability of drawing a random sample in which X = 51.5, s = 18, and N =21 from a population where M = 55?

• 10. What is the probability of drawing a sample of 144 with a mean of 50 or larger and a standard deviation of 5 from a population with a mean of 49?

• 11. It is common for manufacturers of machines that measure to describe the tolerance levels of their machines. For example, a company that manufactures odometers (that measure mileage on a car) would want to know how accurate their equipment is. (The federal government, which allows tax deductions based on mileage, also is interested in such information.) Suppose 100 new cars (with new odometers) traveled over a 100-mile course (as determined by surveying) and the following statistics were obtained. Establish a 95% confidence interval about the mean and carefully explain in a sentence the interpretation of the confidence interval.

X=100.9 s = 2.3 N = 100

Write the z scores you would use if you were asked to establish a 90% confidence interval.