Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

A spinner has five equal sections that are numbered 1 through 5.

In which distributions does the variable X have a binomial distribution?

Select EACH correct answer.




When the spinner is spun three times, X is the sum of the numbers the spinner lands on.

When the spinner is spun multiple times, X is the number of spins until it lands on 5.

When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.

When the spinner is spun five times, X is the number of times the spinner lands on 1.

Answer 1

Answer: C & D

Explanation:

A binomial experiment must satisfy ALL four of the following:

1. A fixed number of trials
2. Each trial is independent of the others
3. There are only two outcomes (Success & Fail)
4. The probability of each outcome remains constant from trial to trial.

A) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.

→ #3 is not satisfied (#4 is also not satisfied)

B) When the spinner is spun multiple times ...

→ #1 is not satisfied

C) When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.

→ Satisfies ALL FOUR

1. A fixed number of trials = 4
2. Each trial is independent of the others = each spin is separate
3. There are only two outcomes = Not Odd & Odd
4. The probability of each outcome remains constant from trial to trial = P(X = not odd) = 0.50 for each spin

D) When the spinner is spun five times, X is the number of times the spinner lands on 1.

→ Satisfies ALL FOUR

1. A fixed number of trials = 5
2. Each trial is independent of the others = each spin is separate
3. There are only two outcomes = 1 & Not 1
4. The probability of each outcome remains constant from trial to trial = P(X = 1) = 0.17 for each spin