Chapter 5

For a normal distribution where the mean is 50 and the standard deviation is 10 , what percentage of the area is a. between the scores of 40 and $47?$ b. above a score of 47 ? $\mathbf{c}$. below a score of 53 ? d. between the scores of 35 and 65 ? $e_{\ast }$ above a score of 72 ? $\mathbf{f}$. below a score of 31 and above a score of 69 ? g. between the scores of 55 and 62 ? h. between the scores of 32 and 47 ?

For a math test on which the mean score was 59 and the standard deviation was 4 , what is the probability that a student randomly selected from this class will have a score a. between 55 and 65 ? b. between 60 and 65 ? C. above 65 ? d. between 60 and 50 ? e. between 55 and 50 ? f. below 55 ?

The local police force gives all applicants an entrance exam and accepts only those applicants who score in the top $15\mathrm{\%}$ on this test. If the mean score this year is 87 and the standard deviation is 8, would an individual with a score of 110 be accepted?

In a distribution of scores with a mean of 35 and a standard deviation of 4, which event is more likely: that a randomly selected score will be between 29 and 31 or that a randomly selected score will be between 40 and $42?$