Question

Ted is not particularly creative. He uses the pickup line​ "If I could rearrange the​ alphabet, I'd put U and I​ together." The random variable x is the number of women Ted approaches before encountering one who reacts positively. Determine whether a probability distribution is given. If a probability distribution is​ given, find its mean and standard deviation. If a probability distribution is not​ given, identify the requirements that are not satisfied.

x P(x)

0 0.001

1 0.008

2 0.029

3 0.062

Does the table show a probability​ distribution? Select all that apply.

A. ​Yes, the table shows a probability distribution.

B. No, the random variable x is categorical instead of numerical.

C. ​No, the sum of all the probabilities is not equal to 1.

D.​No, not every probability is between 0 and 1 inclusive.

E. ​No, the random variable​ x's number values are not associated with probabilities.

Find the mean of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. mu μ = _________ women ​(Round to one decimal place as​ needed.)

B. The table does not show a probability distribution.

Find the standard deviation of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.sigma σ = _______ women ​(Round to one decimal place as​ needed.)

B. The table does not show a probability distribution.

Answer 1

For any distribution to be a valid probability distribution,

All the probabilities should be between 0 and 1, inclusive and the sum of all the probabilities should be equal to 1. Here,

The probabilities are between 0 and 1 so first condition is satisfied.

Sum = 0.001 + 0.008 + 0.029 + 0.062 = 0.1

Which is not equal to 1. Hence, this is not a valid probability distribution.

Therefore,

a) Option C is correct.

Mean: Option B is correct.

Standard deviation: Option B is correct.