A study was conducted and found that bags of original Skittles contain approxima

Question

A study was conducted and found that bags of original Skittles contain approximately 19% red candies. You have five bags of candy and select one candy from each bag. The random variable x represents the number of red candies selected. The selected candy can be classified as either being red (R) or not being red (N).

1. Is this a binomial experiment? If so, explain why and identify the numerical values for the variables required.

2. Construct a discrete probability distribution for this experiment. In order to find the probability for each x value, you need to use the appropriate discrete probability formula separately for each x-value; therefore, you should be using the formula six different times. For full credit, along with showing your table for the discrete probability distribution, you must separately show the setup of the probability formula and your calculations for each x-value.

Explanation / Answer

a.
Binomial Experiment-
A binomial experiment (also known as a Bernoulli trial) is a statistical experiment that has the following properties:
1.The experiment consists of n repeated trials.
2.Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure.
3.The probability of success, denoted by P, is the same on every trial.
4.The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials.
b.
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials   
n = is the number of independent trials   
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 5 * 0.19
= 0.95
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 5 * 0.19 * 0.81
= 0.7695
III.
standard deviation = sqrt( variance ) = sqrt(0.7695)
=0.8772
no. of red candy from a selected 5 candy can be of 0 OR 1 OR 2 OR 3 OR 4 OR 5
P( X = 0 ) = ( 5 0 ) * ( 0.19^0) * ( 1 - 0.19 )^5
= 0.3487
P( X = 2 ) = ( 5 2 ) * ( 0.19^2) * ( 1 - 0.19 )^3
= 0.1919
P( X = 3 ) = ( 5 3 ) * ( 0.19^3) * ( 1 - 0.19 )^2
= 0.045
P( X = 4 ) = ( 5 4 ) * ( 0.19^4) * ( 1 - 0.19 )^1
= 0.0053
P( X = 5 ) = ( 5 5 ) * ( 0.19^5) * ( 1 - 0.19 )^0
= 0.0002

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