Question

1

A fair coin is flipped 15 times. Each flip is independent. What is the probability of getting more than ten heads?

Let X = the number of heads in 15 flips of the fair coin. X takes on the values 0, 1, 2, 3, ..., 15. Since the coin is fair, p = 0.5 and q = 0.5. The number of trials is n = 15. State the probability question mathematically.

2

Approximately 70% of statistics students do their homework in time for it to be collected and graded. Each student does homework independently. In a statistics class of 50 students, what is the probability that at least 40 will do their homework on time? Students are selected randomly.

a. This is a binomial problem because there is only a success or a __________, there are a fixed number of trials,

and the probability of a success is 0.70 for each trial.

b. If we are interested in the number of students who do their homework on time, then how do we define X?

c. What values does x take on?

d. What is a "failure," in words?

e. If p + q = 1, then what is q?

f. The words "at least" translate as what kind of inequality for the probability question P(x ____ 40).

Answer 1

1. Here events are independent, only two outcomes, p=0.5 is same for all and n is constant

Hence all the properties of binomial are satisfied

So we will use binomial distribution excel formula to find required probability

2. a. This is a binomial problem because there is only a success or a failure, there are a fixed number of trials,

b. x is number of students who do their homework on time

c. x=0,1,2,3,4,........,40

d. q is probability of students who do not do their homework in time for it to be collected and graded.

e. q=1-p=1-0.70=0.30

f.