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 (based on a Microsoft Instant Messaging survey).

x P(x)

0 0.091

1 0.334

2 0.408

3 0.166

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.

This data is not a probability distribution

The reason sum of the probabilities is not equal

∑ P(X=x) ≠ 1

Step-by-step explanation:

Explanation:-

Given data

x         0            1                  2              3

p(x)    0.091    0.334          0.408      0.166

Discrete distribution :-

Probability distribution of a random variable is the set of its possible values together with their respective probabilities. Suppose X is a discrete random variable with possible outcomes (values) x₁ , x₂ , x₃ ,......... The probability of each possible outcome

If the numbers  satisfy the two conditions

i)

ii) ∑P(X=x) =1

Given data condition(i) satisfied

but the condition (ii) is not satisfied

0.091+0.334+ 0.408+ 0.166 = 0.999

sum off all probabilities is not equal to one

Conclusion:-

The given data is not probability distribution

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

2.2°  

step-by-step explanation:

let θ = the angle of elevation.

tanθ =77/2020

tanθ = 0.038 12

      θ = tan⁻¹0.038 12

      θ = 2.2°