Question

The probability that Ariana is on time for a given class is 69 percent. If there are 39 classes during the semester, what is the best estimate of the number of times out of 39 that Ariana is on time to class

Answer 1

Answer:

The best estimate of the number of times out of 39 that Ariana is on time to class is 27.

Step-by-step explanation:

For each class, there are only two possible outcomes. Either Ariana is on time, or she is not. The probability of Ariana being on time for a class is independent of other classes. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$

The probability that Ariana is on time for a given class is 69 percent.

This means that $p = 0.69$

If there are 39 classes during the semester, what is the best estimate of the number of times out of 39 that Ariana is on time to class

This is E(X) when n = 39. So

$E(X) = np = 39*0.69 = 26.91$

Rounding

The best estimate of the number of times out of 39 that Ariana is on time to class is 27.