intro to statistics

Question

At a certain school, approximately 65% of statistics students do their homework in time for it to be collected and graded. Assume that each student does homework independently.



1. (a) In a class of 40 students, how many do their homework on time?
2. (b) In a class of 40 students, what is the probability that more than 28 will do their homework on time?
3. (c) In a class of 40 students, what is the probability that at most 28 will do their homework on time?

Answer 1

Let p = 0.65 (65% of students turned in homework on time). Our sample size will be 40 students in a class.

1. You will need to find the expected value of students turning in their homework on time.

E[X] = np = (40)(0.65) = 26

26 students turned in their homework on time.

2. You will need to set up the formula for the binomial cdf.

P(X > 28) = Σ⁴⁰_x=28 C(40, x)*(0.65)^x*(0.35)^40-x = 0.2053

The probability that more than 28 students will turn in their homework on time is about 0.2053.

3. You will need to use the complement rule since all probabilities add up to 1.

P(X ≤ 28) = 1 - P(X > 28) = 1 - [Σ⁴⁰_x=28 C(40, x)*(0.65)^x*(0.35)^40-x]= 1 - 0.2053 = 0.7947

The probability that at most 28 students will turn in their homework on time is about 0.7947.