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?


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.


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


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

Homework Answers

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
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