Dr. Wilson is considering investing a fixed sum of money in each of three business ventures. Assume that the probability distribution for the number of successful ventures out of three is as follows:                                X                            P(X)                    0                               .022                    1                               .194                   2                                .434                   3                                .350 What is the expected value for the number of successful ventures?What is the standard deviation for the number of successful ventures?What is the probability that Dr. Wilson will enjoy at least two successful ventures?What is the probability that Dr. Wilson will enjoy no successful ventures?

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Asked Feb 13, 2020
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Dr. Wilson is considering investing a fixed sum of money in each of three business ventures. Assume that the probability distribution for the number of successful ventures out of three is as follows:

 

 

                              X                            P(X)

 

  •                    0                               .022
  •                     1                               .194
  •                    2                                .434
  •                    3                                .350

 

What is the expected value for the number of successful ventures?

What is the standard deviation for the number of successful ventures?

What is the probability that Dr. Wilson will enjoy at least two successful ventures?

What is the probability that Dr. Wilson will enjoy no successful ventures? 

 

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Expert Answer

Step 1

The random variable X denotes the number of defects. The formula for mean, variance and standard deviation is given by:

Statistics homework question answer, step 1, image 1

Step 2

Mean of the random variable is,

Statistics homework question answer, step 2, image 1

The variance of the random variable is,

Statistics homework question answer, step 2, image 2

Step 3

The standard deviation of the random variable is,

Statistics homework question answer, step 3, image 1

The probability that Dr. Wilson will enjoy at least two successful ventures is as follows:

Statistics homework question answer, step 3, image 2

...

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