Question

Question 1:

A bin of 100 travel clocks are tested to see if they work properly, knowing that 5% of them are defective. The clocks are checked until a defective clock is found.
a) Explain why this situation cannot be modelled using a binomial distribution.
b) Describe how to change this situation so that it can be modelled using a binomial distribution.

Question 2:

Model each of the following situations using a binomial distribution. Identify the discrete random variable, X; the number of trials, n; the probability of success, p; and the probability of failure, q, in any trial.
a) A game consists of rolling a die eight times. You win if the result is 5 or 6. You record the number of wins.
b) A stand of 500 trees is infected by a particular insect. The chance of survival is 30%. The number of surviving trees is recorded.

Answer 1

Question 1:

(a)
This situation cannot be modeled using a binomial distribution because the Total number of trials is not constant, since the experiment is stopped when a defective clock is found.

(b)

We can change the situation as follows

A bin of 100 travel clocks are having 5% defective. 10 clocks are selected. and number of defectives are noted.

Here

n = 10

p =0.05

q = 1 - p = 0.95

Question 2:

(a)

Discrete Random Variable = X = getting 5 or 6

Number of trials = 8

Probability of success = 1/3

probability of failure = 2/3

(b)

Discrete Random Variable = X = Surviving of a tree

Number of trials = 500

Probability of success = 0.30

Probability of failure = 0.70