In the following probability distribution, the random variable x represents the number of activities a parent of a 6 th dash to 8 th -grade student is involved in. complete parts (a) through (f) below.
x 0 1 2 3 4
p(x) 0.216 0.072 0.322 0.289 0.101
compute and interpret the mean of the random variable x.
the mean is activities.
(type an integer or a decimal.)
(d) compute the standard deviation of the random variable x.
the standard deviation is activities.
(round to one decimal place as needed.)
(e) what is the probability that a randomly selected student has a parent involved in three activities?
the probability is (type an integer or a decimal.)
(f) what is the probability that a randomly selected student has a parent involved in three or four activities?
the probability (type an integer or a decimal.)

Applying statistical concepts, we have that:

c) The mean is of 1.987 activities.

d) The standard deviation is of 1.67 activities.

e) The probability is 0.289.

f) The probability is 0.39.

The probability distribution is given by:

Item c:

The mean is given by the sum of the multiplications of each outcome by it's probability, thus:

The mean is of 1.987 activities.

Item d:

The standard deviation is given by the square root of the sum of the squares of each outcome subtracted by the mean, multiplied by it's probability, thus:

The standard deviation is of 1.67 activities.

Item e:

This probability is P(X = 3), thus 0.289.

Item f:

This probability is:

A similar problem is given at link

The mean/expected value is

d. The standard deviation is the square root of the variance, which itself is

We have

Then the variance is

and so the standard deviation is

e. We know this immediately from the table:

f. A parent can be involved in either 3 or 4 activities, but not simultaneously 3 and 4 activities (i.e. these events are disjoint), so

the answer is 99.

answer: i wpould go with c

step-by-step explanation: