Suppose that IQ scores have a bell-shaped distribution with a mean of 99 and a standard deviation of 12. Using the empirical rule, what percentage of IQ scores are less than 87? Please do not round your answer.

87-99 = -12/12 = -1

I get stuck here. I know 1 standard deviation lies between 68%.

87 is 1 SD below mean. 68% are

±1 SD, therefore 34% are below the mean, leaving 50% - 34% = 16%

Here is another way to figure it out exactly.

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. Multiply by 100 to get percentage.

To determine the percentage of IQ scores that are less than 87, we need to use the empirical rule, which states that:

- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.

Since 87 is one standard deviation below the mean of 99, we can say that approximately 68% of IQ scores are greater than or equal to 87.

Therefore, the percentage of IQ scores that are less than 87 is approximately 32%.

To calculate the percentage of IQ scores that are less than 87, we can use the empirical rule, also known as the 68-95-99.7 rule, which applies to data that follow a bell-shaped or normal distribution. According to the empirical rule:

- Approximately 68% of the data lies within one standard deviation of the mean.
- Approximately 95% of the data lies within two standard deviations of the mean.
- Approximately 99.7% of the data lies within three standard deviations of the mean.

In this case, we know that the mean is 99 and the standard deviation is 12. We want to find the percentage of IQ scores that are less than 87.

To calculate this, we need to determine how many standard deviations below the mean 87 is. We can do this by subtracting the mean from 87 and dividing the result by the standard deviation:

(87 - 99) / 12 = -12 / 12 = -1

Therefore, 87 is one standard deviation below the mean.

Since approximately 68% of the data lies within one standard deviation of the mean, we can conclude that approximately 68% of IQ scores are less than 87.

So, the answer is 68%.

16%