Question

In: Statistics and Probability

The average GPA at the University of North Carolina is 3.2, with a standard deviation of...

The average GPA at the University of North Carolina is 3.2, with a standard deviation of 0.3. Assume that all GPAs at the University of North Carolina are normally distributed.

What is the probability of randomly selecting a student at the University of North Carolina with a GPA of 2.9 or lower? Possible answers: A. 0.10 B. 0.16 C. 0.24 D. 0.31

What is the probability of randomly selecting a student at the University of North Carolina with a GPA between 2.9 and 3.5? Possible answers: A. 0.34 B. 0.68 C. 0.75 D. 0.95

What is the probability of randomly selecting a student at the University of North Carolina with a GPA higher than 3.7? Possible answers: A. 0.023 B. 0.048 C. 0.058 D. 0.977

Expert Solution

What is the probability of randomly selecting a student at the University of North Carolina with a GPA of 2.9 or lower?

Solution:

And

And we know that using empirical rule that is 68-95-99.7 percent of the area lies in one sigma, two sigma and three sigma units respectively.

Therefore, 68% of the area lies between 2.9 and 3.5.

Remaining 32% will be out of one sigma limits such that 16% will be less than 2.9 and 16% will be greater than 3.5

Therefore the answer will be 0.16

What is the probability of randomly selecting a student at the University of North Carolina with a GPA between 2.9 and 3.5?

Solution:

And

And we know that using empirical rule that is 68-95-99.7 percent of the area lies in one sigma, two sigma and three sigma units respectively.

Therefore, 68% of the area lies between 2.9 and 3.5.

Therefore the answer will be 0.68

What is the probability of randomly selecting a student at the University of North Carolina with a GPA higher than 3.7?

And we know that using empirical rule that is 95 percent of the area lies in two sigma units.

Which means 5% willl be out of two sigma limits. And 2.5% will be higher than that of 3.8.

that is probabaility should be 0.025 but here the value is slightly less than that of 3.8 which will cover little more area higher than 3.7.

Therefore the answer will be 0.048

orchestra answered 2 years ago

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