A professional basketball star who had a reputation for being a poor free throw shooter made 5000 of the 9747 free throws that heattempted, for a success ratio of 0.513. A simulation was developed to generate random numbers between 1 and 1000. An outcome of 1 through 513 was considered to be a free throw that ismade, and an outcome of 514 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).

1 0 1 1 0

a. Is the proportion of successful free throws P from the simulation reasonably close to the value of 0.513? (Hint: A proportion is said to be"reasonably close" if it is within the given success ratio the probability of a singleevent.)

No, P isnot reasonably close to the value of 0.513.

Yes, P is reasonably close to the value of 0.513.

b) The simulation was conducted 10 times to generate five resultsR1, R2,R3, R4 and R5 eachtime, as shown in the table below. Determine the proportion of successful free throws P in each case.

Case

R1 R2 R3 R4 R5 P

1 1 0 1 1 0

2 0 0 0 0 1

3 1 1 0 1 0

4 0 0 1 0 0

5 0 1 0 0 1

6 0 1 1 0 0

7 1 1 0 1 1

8 0 0 1 1 1

9 1 1 0 0 0

10 0 0 0 1 0

(Do notround.)