1. (8 points) From the following set of questions provide a comprehensive soluti

Question

1. (8 points) From the following set of questions provide a comprehensive solution set, show your work and explain why an answer is correct.

2. (7 points) For the the other answer choices that you believe to be incorrect, explain why they are incorrect. Be thorough.

1 TRUE or FALSE: The probability of the sample space is always equal to 1.

TRUE

FALSE

2 TRUE or FALSE: The normal distribution is defined by two parameters and

TRUE

FALSE

3 Suppose a company that makes video game consoles samples 20 consoles for inspection. The probability a gaming console fails prior to the end of the warranty period is 0.08 and the failure of a console is independent between consoles. What type of distribution will best model the number of consoles out of the 20 that will fail prior to the end of the warranty period?

A Poisson

B Exponential

C Normal

D Binomial

Explanation / Answer

Result:

1. (8 points) From the following set of questions provide a comprehensive solution set, show your work and explain why an answer is correct.

2. (7 points) For the the other answer choices that you believe to be incorrect, explain why they are incorrect. Be thorough.

1 TRUE or FALSE: The probability of the sample space is always equal to 1.

Answer: TRUE

FALSE

The sample space is the collection of all possible outcomes of the event. Probability of sample space is number of all possible events divided by number of all possible events which is 1.

2 TRUE or FALSE: The normal distribution is defined by two parameters and

Answer: TRUE

FALSE

Normal distributions are defined by two parameters, the mean (?) and the standard deviation (?),

where ? is the location parameter and ? is the scale parameter.

3 Suppose a company that makes video game consoles samples 20 consoles for inspection. The probability a gaming console fails prior to the end of the warranty period is 0.08 and the failure of a console is independent between consoles. What type of distribution will best model the number of consoles out of the 20 that will fail prior to the end of the warranty period?

A Poisson

B Exponential

C Normal

answer D Binomial

Assumptions of the binomial distribution

1.There are a fixed number of trials. Here we are having 20 consoles, n=20 fixed

2.This has 2 outcomes (called fails and not fails)

3.The trials are all independent of one another. Here failure of a console is independent between consoles

4. The probability of success is the same for all trials. (here probability is represented by 0.08).

All the assumptions for binomial are fulfilled here

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