Question

Short steps please 8) Determine whether the following random variable is a binomial? a. Seven hockey players attempt to make a goal. Let X be the number of goals made. Binomial? (yes or no) If not, state which condition was not met. b. A fair coin is tossed 12 times. Let X be the number of times the coin lands on heads. Binomial? (yes or no) If not, state which condition was not met.

Answer 1

For a variable to be a binomial random variable, ALL of the following conditions must be met:

i) There are a fixed number of trials (a fixed sample size).

ii) On each trial, the event of interest either occurs or does not.

iii) The probability of occurrence (or not) is the same on each trial.

iv) Trials are independent of one another.

a) Therefore, this is not Binomial.

Answer

No

Reason:

There are no fixed number of trials.

b) Yes, this is binomial.