Using the frequency table below what is the estimate of the probability that pat
ID: 3244747 • Letter: U
Question
Using the frequency table below what is the estimate of the probability that pat will make fewer than 5 free throws in tries and what is the average number of free throws made?
pat is basketball player with a career 60% free throws shooting percentage. Describe a simulation model to determine the number of free throws pat can expect to make out of 10 tries. discuss what you would put in the calculate and whatthe digits represent
(a)run five trials of your simulation and addyour result to the frequency table below so that there is total of 400 trails. record the total result in the "frequency after) column
395
Nummber made Frequency before Frequency after 1 1 1 2 3 3 3 10 11 4 40 40 5 101 102 6 140 140 7 67 69 8 16 17 9 15 15 10 2 2 Total395
Explanation / Answer
Solution
Probability that Pat will make fewer than 5 free throws
= (Number of cases where number of free throws is less than 5)/Total frequency
= (1 + 3+ 10 + 40)/395 = 54/395 = 0.1367 ANSWER 1
The average number of free throws made = [1,10](x.f), where f is the frequency of x free throws, x = 1, 2, ….. , 10.
= 2294/395 = 5.81 ANSWER 2
Computations are given in the table below:
Number made x
Frequency before f
x.f
1
1
1
2
3
6
3
10
30
4
40
160
5
101
505
6
140
840
7
67
469
8
16
128
9
15
135
10
2
20
Total
395
2294
Average = 2294/395 =
5.807595
Procedure for simulation
Pick 10 single-digit random numbers starting from a random point on a Random Number Table and continue in sequence. If the number picked is 1, 2, 3, 4, 5 or 6, treat it as a free throw. If it is 7, 8, 9 or 0, treat it as a non-free throw.
Count the number of free throws as above and that gives the number of free throws in 10 tries.
Repeat the above two steps 5 times and record the result as in the following table:
Run #
Random digit
# free throws
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
Number made x
Frequency before f
x.f
1
1
1
2
3
6
3
10
30
4
40
160
5
101
505
6
140
840
7
67
469
8
16
128
9
15
135
10
2
20
Total
395
2294
Average = 2294/395 =
5.807595
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