Question

Suppose the data have a bell-shaped distribution with a mean 35 of and a standard deviation of 7. Use the empirical rule to determine the percentage of data within of the following range: 21 to 49

Answer 1

Approximately 95% of the data falls within two standard deviations of the mean in a bell-shaped distribution.

Step-by-step explanation:

The empirical rule states that in a bell-shaped distribution, approximately 95% of the data falls within two standard deviations of the mean. In this case, the mean is 35 and the standard deviation is 7. To find the percentage of data within the range of 21 to 49, we need to calculate how many standard deviations away these values are from the mean.

First, we calculate the difference between the lower bound (21) and the mean (35): 21 - 35 = -14. Then, we divide this difference by the standard deviation: -14 / 7 = -2.

Next, we calculate the difference between the upper bound (49) and the mean (35): 49 - 35 = 14. Then, we divide this difference by the standard deviation: 14 / 7 = 2.

Since the range from -2 to 2 represents two standard deviations, we can conclude that approximately 95% of the data falls within this range.