Suppose that IQ scores have a bell-shaped distribution with a mean of 95
95
and a standard deviation of 18
18
. Using the empirical rule, what percentage of IQ scores are at least 149
149
? Please do not round your answer.
149 - 95 = 54 ... 54 / 18 = 3
what percentage of values is at least 3 standard deviations above the mean?
To find the percentage of IQ scores that are at least 149 using the empirical rule, we need to determine which percentage falls within 1.5 standard deviations above the mean.
First, we calculate the range of scores within 1.5 standard deviations above the mean:
1.5 * 18 = 27
Next, we add this range to the mean to find the upper bound:
95 + 27 = 122
Now, we can calculate how many standard deviations away 149 is from the mean:
(149 - 95) / 18 = 3
Since 149 is 3 standard deviations away from the mean, it falls outside the range of 1.5 standard deviations above the mean.
According to the empirical rule, approximately 68% of the scores fall within 1 standard deviation of the mean. However, since 149 is 3 standard deviations away, it is beyond the range for the empirical rule.
Therefore, we cannot use the empirical rule to directly calculate the percentage of IQ scores that are at least 149.