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Chapter 9: Problem 552

Suppose that \(75 \%\) of the students taking statistics pass the course. In a class of 40 students, what is the expected number who will pass. Find the variance and standard deviation.

Short Answer

Expert verified
In the given statistics class, we expect 30 students to pass the course, with a variance of 7.5 and a standard deviation of approximately 2.74 students.

Step by step solution

01

Calculate the expected number of students who will pass

Using the formula for the expected value of a binomial distribution: Expected value (mean) = n * p = 40 students * 0.75 probability of passing = 30 students The expected number of students who will pass the course is 30.
02

Calculate the variance

Next, we use the formula for the variance of a binomial distribution: Variance = n * p * (1-p) = 40 students * 0.75 probability of passing * 0.25 probability of failing = 7.5 The variance is 7.5.
03

Calculate the standard deviation

Finally, we use the formula for the standard deviation, which is the square root of the variance: Standard deviation = sqrt(variance) = sqrt(7.5) ≈ 2.74 The standard deviation is approximately 2.74 students. In conclusion, we expect 30 students to pass the course, with a variance of 7.5, and a standard deviation of approximately 2.74 students.

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