Question

A survey asked 1654 people how many hours per day they were able to relax, and the results were as follows:

Number of
Hours
0
1
2
3
4
5
6
7
Frequency
120
175
254
302
298
200
213
92
Consider these students as the population, and let the random variable be the number of hours of relaxation for a
person sampled at random from this population. Construct the probability distribution. (Round all probability values
to four decimal places)

Answer 1

To construct the probability distribution, we need to calculate the probability for each value of the random variable.

The probability of a person having a certain number of hours of relaxation (X) can be calculated by dividing the frequency of that value by the total number of people surveyed (1654).

X | P(X)

0 | 120/1654 1 | 175/1654 2 | 254/1654 3 | 302/1654 4 | 298/1654 5 | 200/1654 6 | 213/1654 7 | 92/1654

Let's calculate these probabilities:

X | P(X)

0 | 0.0726 1 | 0.1058 2 | 0.1537 3 | 0.1826 4 | 0.1802 5 | 0.1209 6 | 0.1289 7 | 0.0557

Rounded to four decimal places, the probability distribution is as follows:

X | P(X)

0 | 0.0726 1 | 0.1058 2 | 0.1537 3 | 0.1826 4 | 0.1802 5 | 0.1209 6 | 0.1289 7 | 0.0557