Question

A study shows that 84​% of the population of all calculus students consider calculus an exciting subject. Suppose 29 students are randomly and independently selected from the population. If the true percentage is really 84​%, find the probability of observing 28 or more of the students who consider calculus to be an exciting subject in the sample of 29. Round to six decimal places.

Answer 1

P = 0.041553

Explanation:

Probability that a student considers calculus exciting. = 0.84

Probability that a student finds calculus not exciting = 0.16

This is a binomial experiment.

p = 0.84 and n = 29

The probability of observing 28 or more of the students who consider calculus to be an exciting subject in our sample of 29 is given by:

`\left(\begin{array}{ccc}29\\28\end{array}\right) .0.84^(28) .0.16^(1)+\left(\begin{array}{ccc}29\\29\end{array}\right) .0.84^(29) .0.16^(0)`

P = 0.041553