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A professional basketball star who had a reputation for
being a poor free throw shooter made 4955 of the 9753
free throws that he attempted, for a success ratio of 0.508.
A simulation was developed to generate random numbers
between 1 and 1000. An outcome of 1 through 508 was
considered to be a free throw that is made, and an
outcome of 509 through 1000 was considered to be a free
throw that is missed. The list below shows the results for
five generated numbers where 1 represents a free throw
that was made and 0 represents a free throw that was
missed. Complete parts (a) and (b).
11
000
a. Is the proportion of successful free throws P
from the simulation reasonably close to the value
of 0.508? (Hint: A proportion is said to be
"reasonably close" if it is within the given success
ratio the probability of a single event.)
O
O
Yes, P is reasonably close to the value of
0.508.
No, P is not reasonably close to the value of
0.508.
b. The simulation was conducted 10 times to
generate five results R1, R2, R3, R4 and R5 each
time, as shown in the table below. Determine the
proportion of successful free throws P in each
case.
Case
1
2
3
4
7
89
R1
1
0
0
0
1
0
0
R2 R3
1
0
1
1
1
1
1
ооо.
1
1
R4 R5
0 0
1
0
1
1
0 0
1
0 1
0 0
0
0
1
0
01
005
1
0
1
0
P
Li
