A professional basketball star who had a reputation for being a poor free throw shooter made 4916 of the 9812 free throws that heattempted, for a success ratio of 0.501. A simulation was developed to generate random numbers between 1 and 1000. An outcome of 1 through 501 was considered to be a free throw that ismade, and an outcome of 502 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).

Is the proportion of successful free throws P from the simulation reasonably close to the value of 0.501? (Hint: A proportion is said to be"reasonably close" if it is within the given success ratio the probability of a singleevent.)

Yes, P is reasonably close to the value of 0.501.

No, P isnot reasonably close to the value of 0.501.

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

1

1

0

1

nothing

2

1

0

0

1

1

nothing

3

0

1

0

0

0

nothing

4

0

1

1

1

0

nothing

5

1

0

0

0

0

nothing

6

1

1

0

0

0

nothing

7

1

0

1

0

1

nothing

8

0

0

0

0

1

nothing

9

1

0

1

0

1

nothing

10

0

0

1

1

1

nothing

(Do notround.)

Based on the aboveresults, would it be unusual for the professional basketball star to make all of five free throws in agame?

No

Yes