Question

A set of data whose histogram is extremely skewed yields a sample mean and standard deviation of 69.5 and 10.75, respectively. What is the minimum percentage of observations that:

A. are between 48 and 91.

and

B. are between 37.25 and 101.75

Answer 1

Using Chebyshev's Rule, we can conclude that there are at least 75% of observations between 48 and 91 and at least 89% of observations between 37.25 and 101.75 for a skewed dataset.

Step-by-step explanation:

For a skewed data set, we can apply Chebyshev's Rule to find the minimum percentage of observations within a certain range of the mean, as the distribution is not bell-shaped and symmetric.

• A. To find the minimum percentage of observations between 48 and 91, we calculate how many standard deviations each value is from the mean (69.5). For 48, which is (69.5-48)/10.75 standard deviations away, it is approximately two standard deviations. For 91, which is (91-69.5)/10.75 standard deviations away, it's about two standard deviations as well. By Chebyshev's Rule, at least 75% of the data lies within two standard deviations of the mean.
• B. For observations between 37.25 and 101.75, this range is three standard deviations from the mean – (69.5-37.25)/10.75 and (101.75-69.5)/10.75. According to Chebyshev's Rule, at least 89% of the data lies within three standard deviations of the mean.

Therefore, we can conclude:

1. There are at least 75% of observations between 48 and 91.
2. There are at least 89% of observations between 37.25 and 101.75.

Answer 2

I am a beautiful person who can help you with the new one of those who are interested