Question 4:

a) For a normal population distribution, a score of -8 is .75 standard deviations above the mean and a score of -5 is 1.4 standard deviations above the mean. What is the mean and standard deviation for this population?

Q. Question 5: A population of scores on a second-year statistics course is normally distributed with a mean of 65 and a standard deviation of 14.

a) What is the probability that an individual drawn randomly from the population would have a score greater than 70?

b) What is the probability that 49 individuals drawn randomly from the population would have an average score greater than 70?

c) What means are associated with the middle 66.8% of the sampling distribution for a sample size of 16 individuals?

d) Suppose you are conducting an experiment that requires a sample of individuals whose mean is within 1/2 standard deviation of the population mean. What sample size should you need to have a 95% chance of satisfying this criterion?

Question 6: 225 students are writing the final exam in Dr. Strangepork's course on statistics. Use the same population parameters as Question 5 (i.e.,mean=65 and standard deviation = 14 ).

a) What T-score is associated with an exam grade of 62?

b) What score on the final exam would be associated with a T-score of 61?

c) Dr. Strangepork decides to curve (rescale) the grades so that the new mean will be 75 and the new standard deviation will be 8. Determine the new scores for original scores of 86 and 44. Who benefited more from the rescaling?