Question

# A biased coin (one that is not evenly balanced) is tossed 6 times. The probability of...

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?

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.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

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

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