Show all work Just the answer without supporting work will r

Show all work. Just the answer, without supporting work, will receive no credit.
The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
18. What is the probability that a randomly selected person has an IQ between 85 and 115? (10 pts)
19. Find the 90th percentile of the IQ distribution. (5 pts)
20. If a random sample of 100 people is selected, what is the standard deviation of the sample mean?
(5 pts)

Solution

By the 68-95-99.7 rule, 68% of all adults will have an IQ within 1 standard deviation of the mean (between 100 - 15 = 85 and 100 + 15 = 115). Since the IQ scores are normally distributed, it is equally likely to have an IQ of between 85 and 100 as it is to have an IQ of between 100 and 115, so 68/2 = 34% of all adults have an IQ of between 100 and 115. Then, due to the symmetry of the bell curve, 50% of all adults will have an IQ of less than 100 (since 100 is the mean), so the required probability is 50 + 34 = 84%.
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Alternatively, you can use a z-table to compute:
P(x ? 115) = P(z ? (115 - 100)/15) = P(z ? 1).