91影视

To show that the probability distribution is a legitimate probability distribution.

Determine the sum of probabilities as follows:

Sum of probabilities $=0.68+0.05+0.08+0.05+0.01+0.02$

=1

The probability range from 0 to ,1 and the sum of the probabilities equals 1.
As a result, the probability distribution provided is a legitimate probability distribution.

To make a histogram of the probability distribution and interpret it.

To histogram of the probability distribution as follows:

The distribution is right-skewed, with the highest bar to the left and a tail of bars to the right.

To describe the event $Y<7$and$P(Y<7)$.

Since,$X<7$ denotes that number of days that people workout is less than 7.
Let, determine $P(X<7)$as follows:

$P(X<7)=P(X=1)+P(X=2)+鈥�..+P(X=6)$

$$\begin{gathered} =0.68+0.05+鈥�..+0.01 \\ =0.98 \end{gathered}$$

As a result, the probability is 0.98

To determine the probability of the event. And to express the event 鈥渨orked out at least once鈥� in terms of Y.

In terms of Y, the event "exercise at least once" may be expressed as $Y鈮�1$

Then $P(Y鈮�1)$

$P(Y鈮�1)=1-P(Y<0)$

$=1-0.68$

$=0.32$

As a result, the probability is 0.32.