Question

A sociologist randomly selects single adults for different groups of​ three, and the random variable x is the number in the group who say that the most fun way to flirt is in person. 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.

Answer 1

I have attached the complete question.

Answer:

Mean; μ = 1.648

Standard deviation;σ = 0.8610

Explanation:

From the image attached, we can see that the probabilities given under the p(x) column are;

0.091

0.334

0.408

0.166

Let's find out if these values give a probability distribution.

ΣP(x) = 0.091 + 0.334 + 0.408 + 0.166

ΣP(x) ≈ 1

Their sum is approximately 1 and they are all between 0 and 1. Thus, it is a probability distribution.

Mean is found by;

μ = ΣxP(x)

From the table attached, x = 0, 1, 2, 3

Thus;

μ = (0 × 0.091) + (1 × 0.334) + (2 × 0.408) + (3 × 0.166)

μ = 1.648

Standard deviation is given by;

σ = √[Σ(x - μ)²•P(x)]

σ = √[((0 - 1.648)² × 0.091) + ((1 - 1.648)² × 0.334) + (2 - 1.648)² × 0.408) + ((3 - 1.648)² × 0.166)]

σ = 0.8610