Question

A basketball player completes a free throw 80% of the time. In practice the player goes to the free throw line
    and takes 5 shots in a row.
    a)   Make a table showing the probability distribution of successes and their probabilities
    b)   Draw the probability histogram.
c) What is the shape of the distribution?
d) What is the mean?
    e) What is the standard deviation?

Answer 1

The number of shots out of which free throw happens could be modelled here as:

a) The probabilities here are computed as:

Using this the probability is computed here as:

X	P(x)
0	0.00032
1	0.0064
2	0.0512
3	0.2048
4	0.4096
5	0.32768

b) Using the above table, the probability histogram here is obtained as:

c) As we can see that there is a tail on the left side of the distribution, therefore this is a case of a left skewed distribution here.

d) The mean here is computed as:
Mean = np = 5*0.8 = 4

Therefore 4 is the required mean here.

e) The standard deviation of the distribution here is computed as:

Therefore 0.8944 is the required standard deviation here.