Question

In an experiment, a fair coin is tossed 4 times and the number of heads that occurs is recorded.

Eighty trials of the experiment are run.
The table shows the frequency of 0, 1, 2, 3, or 4 heads occurring in the trials.
Number of heads
0
1
2
3
4
Frequency
4
8
36
20
12
Create a probability distribution for the discrete variable.
Drag the sliders on the horizontal axis to represent the probability distribution.

Answer 1

Explanation:

Hello!

The experiment consist in "a fair coin is tossed 4 times" the recorded variable is X: number of heads obtained after tossing the coin 4 times

The possible values for this variable: X: 0; 1; 2; 3; 4

The frequencies observed for each possible value of X after repeating the experiment for n=80 times

fi: 4; 8; 36; 20; 12

To create the probability distribution you have to calculate the probability for each value of X, by doing the following calculation
`p(xi)= (fi)/(n)`

p(X=0)= p(0)= 4/80= 0.05

p(X=1)= p(1)= 8/80= 0.10

p(X=2)= p(2)= 36/80= 0.45

p(X=3)= p(3)= 20/80= 0.25

p(X=4)= p(4)= 12/80= 0.15

For this to be a probability of distribution the following conditions are to be met:

• p(xi)≥0
• ∑p(xi)=1

All calculated probabilities are at most zero.

∑p(xi)= 0.05+0.10+0.45+0.25+0.15= 1

xi | 0 | 1 | 2 | 3 | 4

fi | 4 | 8 | 36| 20 | 12

p(xi)| 0.05| 0.10| 0.45| 0.25| 0.15

F(Xi)|0.05| 0.15 | 0.60| 0.85| 1

I hope this helps!