# Statistics, the normal distribution, probability, and standard scores

**Question description**

Over the years, thousands of scores have been collected for
the Wechsler Adult Intelligence Scale. Assume that the distribution of these
scores is normal, with A_{u} = 100 and o=15

a) What proportion of intelligence scores is equal to or greater than 115?

b) What proportion of intelligence scores is less than 70?

c) What proportion of intelligence scores is less than 60?

d) What proportion of scores is in between 100 and 120?

e) What proportion of scores is between 75 and 100?

f) What interval of scores includes the middle 80 percent of scores on the test?

g) If you select the a person at random , what is the probability that his or her intelligence score will be between 90 and 120?

h) If you select the a person at random , what is the probability that his or her intelligence score will be equal or less than 80?

i) If you select a person at random, what is the probability that his or her intelligence score will be equal to or greater than 125?

j) If you select the a person at random , what is the probability that his or her intelligence score will be equal to or greater than 140?

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