Question

If the scores on an IQ Test, Mean=100; sd=15, are normally distributed, what percentage of the normal population would you expect to find between the IQ scores of 70 and 130?

a) 68%
b) 95%
c) 99%
d) 100%

Answer 1

Approximately 95% of the normal population would be expected to fall between the IQ scores of 70 and 130, as this range covers two standard deviations from the mean in a normal distribution.

Correct option is b) 95%

Step-by-step explanation:

If the scores on an IQ Test are normally distributed with a mean of 100 and a standard deviation of 15, the percentage of the normal population we would expect to find between the IQ scores of 70 and 130 is given by the empirical rule (or 68-95-99.7 rule). According to the empirical rule:

• About 68% of the data lies within one standard deviation of the mean (between 85 and 115).
• About 95% of the data lies within two standard deviations of the mean (between 70 and 130).
• About 99.7% of the data lies within three standard deviations of the mean (between 55 and 145).

Since the range from 70 to 130 encompasses two standard deviations on either side of the mean, the correct answer is that 95% of the population falls within this range, which corresponds to option b).