**Question 20:**Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.59 and a standard deviation of 0.39. Using the empirical rule, what percentage of the students have grade point averages that are between 1.42 and 3.76? **Explanation for Educational Website:**To solve this problem, we apply the empirical rule (also known as the 68-95-99.7 rule) which states that for a normal distribution:- About 68% of the data falls within one standard deviation from the mean.- About 95% of the data falls within two standard deviations from the mean.- About 99.7% of the data falls within three standard deviations from the mean.Here, we calculate how many standard deviations 1.42 and 3.76 are from the mean of 2.59:1. **Calculate the number of standard deviations for 1.42:** - $ \text{Lower bound} = \frac{2.59 - 1.42}{0.39} = 3 $ standard deviations below the mean.2. **Calculate the number of standard deviations for 3.76:** - $ \text{Upper bound} = \frac{3.76 - 2.59}{0.39} = 3 $ standard deviations above the mean.Since 1.42 and 3.76 are each 3 standard deviations away from the mean, according to the empirical rule, approximately 99.7% of the students have GPAs in this range.

Mean = 2.59 Standard deviation = 0.39

Suppose that grade point averages of undergraduate students at one university have a bell- shaped distribution with a mean of 2.59 and a standard deviation of 0.39. Using the empirical rule, what percentage of the students have grade point averages that are between 1.42 and 3.76?

Suppose that grade point averages of undergraduate students at one university have a bell- shaped distribution with a mean of 2.59 and a standard deviation of 0.39. Using the empirical rule, what percentage of the students have grade point averages that are between 1.42 and 3.76?

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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