Probability, the normal curve, & z scores

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The state parole board has a policy that it will only release prisoners who meet a minimum amount of time served, have a minimum of good-time points, and have an acceptable score from their drug awareness class. The mean of this distribution is 90 and the standard deviation is 15.

1. For this distribution, what is the range of scores that are between 1 standard deviation below and one standard deviation above the mean? What is the range of scores corresponding to 2 standard deviations below and above the mean?

2. These are some scores from the state parole board policy mentioned earlier.

a. Calculate the z scores for the following data:

90

50

70

100

30

45

For the next 3 questions, “Use the z table under the standard normal curve.”).

b. What proportion of cases have a score of between 90 and 110? Is the probability of getting a score between 90 and 110 high or low?

c. What proportion of cases have a score between 60 and 90? What percentage does this represent? Is the probability of getting a score between 60 and 90 high or low?

d. What proportion of cases have a score that is higher than 135? Is the probability of getting such a score high or low?

p(1)

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