Question

A biased coin (one that is not evenly balanced) is tossed 6 times. The probability of Heads on any toss is

0.3. Let X denote the number of Heads that come up.

1. Does this experiment meet the requirements to be considered a Bernoulli Trial? Explain why or why

not.

2. If we call Heads a success, what would be the parameters of the binomial distribution of X?

(Translation: find the values of n and p)

3. What is the shape of this binomial distribution (right skewed, symmetric, left skewed)? Explain how

you know this.

4. What would be the random-variable notation to represent that exactly 2 Heads are tossed?

5. Using the Binomial Probability Formula and your answers from

questions 1-4, calculate the following:

P(X = 2)

P(1 < X < 5)

*NOTE: Round final answers to 3 decimal places.*

6. Find the mean and standard deviation of X.

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A new drug trial is being tested. The results of the trial show that 90% of the participants are cured of

their disease after using the new drug. (Assume that this does meet the requirements of Bernoulli

Trials.) Suppose you are studying the results of 3 people who participated in the trial.

1. Draw a tree diagram to show the possible outcomes of this study of 3 participants. Be sure to include

the probabilities for each success or failure on the branches of your tree. Include a listing of the

outcome and the probability of each outcome.

2. Construct a probability distribution table to show the number of participants cured of their disease

Answer 1

1. Yes as all the tosses are independent of each other. Also, each toss has just two outcomes, which satisfies the Bernoulli condition.

2. Here n=6 and p=0.3

3. This a right-skewed data.

4. If two heads are tossed then X=2.

5.

6. E(X) = np = 6*0.3 = 0.18

1. Here is the decision tree:

2.

X=x	0	1	2	3
P(X=x)	0.001	0.027	0.243	0.729