Question

At a drop-in mathematics tutoring center, each teacher sees 4 to 8 students per hour. The probability that a tutor sees 4 students in an hour is 0.12;5 students, 0.13; 6 students, 0.30; and 7 students, 0.33. Let be the number of students per hour of a randomly selected teacher.

Answer 1

To find the probability that at least 40 out of 50 students do their homework on time, use the binomial probability formula.

Step-by-step explanation:

To find the probability that at least 40 out of 50 students do their homework on time, we can use the binomial probability formula.

The formula is:

P(X ≥ r) = - P(X < r)

Where P(X ≥ r) is the probability that X is greater than or equal to r, P(X < r) is the probability that X is less than r, and X is a binomial random variable representing the number of students doing their homework on time.

In this case, n = 50 (number of students), p = 0.70 (probability that a student does homework on time), and r = 40 (minimum number of students doing homework on time).

Using the binomial probability formula, we can calculate:

P(X ≥ 40) = 1 - P(X < 40)

To calculate P(X < 40), we can use the binomial probability function on a graphing calculator or an online binomial probability calculator.