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Answer :
We first note that in the simulation a total of 50 random numbers were generated. To mimic a shooter with a 40% success rate, numbers from 1 to 40 (inclusive) indicate a successful shot. Out of these 50 numbers, 18 numbers fell in the range 1 to 40. This gives a proportion of successful simulated shots of
[tex]$$
\frac{18}{50} = 0.36 \quad \text{(or } 36\% \text{)}
$$[/tex]
Now, comparing the different percentages:
1. Mike’s claim is that he is a 40% shooter.
2. The simulation shows that the success rate is 36%.
3. His observed performance was 17 successful shots out of 50 attempts, which is
[tex]$$
\frac{17}{50} = 0.34 \quad \text{(or } 34\% \text{)}.
$$[/tex]
This simulation indicates that, in one instance, 36% of the shots were successful. While 36% is reasonably close to the 40% claimed shooting ability, it is still 4 percentage points lower than his stated ability. Also, his actual shooting performance (34%) is even further below the 40% claim.
Thus, the answer to part (c) is:
- The proportion of random numbers generated that were successful is 36%.
- This simulation result means that, in this one trial, the shooter made 36% of his shots. Compared to Mike’s claim of being a 40% shooter, the simulated shot percentage is 4 percentage points lower, and his observed performance of 34% is even further below the claim.
[tex]$$
\frac{18}{50} = 0.36 \quad \text{(or } 36\% \text{)}
$$[/tex]
Now, comparing the different percentages:
1. Mike’s claim is that he is a 40% shooter.
2. The simulation shows that the success rate is 36%.
3. His observed performance was 17 successful shots out of 50 attempts, which is
[tex]$$
\frac{17}{50} = 0.34 \quad \text{(or } 34\% \text{)}.
$$[/tex]
This simulation indicates that, in one instance, 36% of the shots were successful. While 36% is reasonably close to the 40% claimed shooting ability, it is still 4 percentage points lower than his stated ability. Also, his actual shooting performance (34%) is even further below the 40% claim.
Thus, the answer to part (c) is:
- The proportion of random numbers generated that were successful is 36%.
- This simulation result means that, in this one trial, the shooter made 36% of his shots. Compared to Mike’s claim of being a 40% shooter, the simulated shot percentage is 4 percentage points lower, and his observed performance of 34% is even further below the claim.
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