An engineering student randomly sampled the train arrival times at a nearby train station. Based on the results, the student estimates that 92% of the trains arrived within 2 minutes of their scheduled arrival times. The margin of error for this estimation is 3%. Which of the following is the most appropriate conclusion about all train arrival times at the station, based on the given estimate and margin of error? Choose 1 answer: (A) It is plausible that 89% and 95% of all trains arrive within 2 minutes of their scheduled arrival times. (B) Exactly 92% of all trains arrive within 5 minutes of their scheduled arrival times. (C) The student is 3% sure that most trains arrive within 2 minutes of their scheduled arrival times. D The student is 97% sure that exactly 92% of all trains arrive within 2 minutes of their scheduled arrival times.

Calculate Lower Bound: Calculate the lower bound of the confidence interval using the given estimate and margin of error. Lower bound = Estimate - Margin of error = 92% - 3% = 89%Calculate Upper Bound: Calculate the upper bound of the confidence interval using the given estimate and margin of error. Upper bound = Estimate + Margin of error = 92% + 3% = 95%Compare Confidence Intervals: Compare the calculated confidence interval with the provided answer choices. The confidence interval is from 89% to 95%, which matches answer choice (A).

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An engineering student randomly sampled the train arrival times at a nearby train station. Based on the results, the student estimates that $92 \%$ of the trains arrived within $2$ minutes of their scheduled arrival times. The margin of error for this estimation is $3 \%$ . Which of the following is the most appropriate conclusion about all train arrival times at the station, based on the given estimate and margin of error? $\newline$ Choose $1$ answer: $\newline$ (A) It is plausible that $89 \%$ and $95 \%$ of all trains arrive within $2$ minutes of their scheduled arrival times. $\newline$ (B) Exactly $92 \%$ of all trains arrive within $5$ minutes of their scheduled arrival times. $\newline$ (C) The student is $3 \%$ sure that most trains arrive within $2$ minutes of their scheduled arrival times. $\newline$ (D) The student is $97 \%$ sure that exactly $92 \%$ of all trains arrive within $2$ minutes of their scheduled arrival times.

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Math Problems

Algebra 2

Interpret confidence intervals for population means

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Q. An engineering student randomly sampled the train arrival times at a nearby train station. Based on the results, the student estimates that

92 \%

of the trains arrived within

2

minutes of their scheduled arrival times. The margin of error for this estimation is

3 \%

. Which of the following is the most appropriate conclusion about all train arrival times at the station, based on the given estimate and margin of error?

\newline

Choose

1

answer:

\newline

(A) It is plausible that

89 \%

and

95 \%

of all trains arrive within

2

minutes of their scheduled arrival times.

\newline

(B) Exactly

92 \%

of all trains arrive within

5

minutes of their scheduled arrival times.

\newline

3 \%

sure that most trains arrive within

2

minutes of their scheduled arrival times.

\newline

(D) The student is

97 \%

sure that exactly

92 \%

of all trains arrive within

2

minutes of their scheduled arrival times.

Calculate Lower Bound: Calculate the lower bound of the confidence interval using the given estimate and margin of error. $\newline$ Lower bound = Estimate - Margin of error $\newline$ = $92\% - 3\%$ $\newline$ = $89\%$
Calculate Upper Bound: Calculate the upper bound of the confidence interval using the given estimate and margin of error. $\newline$ Upper bound = Estimate + Margin of error $\newline$ = $92\% + 3\%$ $\newline$ = $95\%$
Compare Confidence Intervals: Compare the calculated confidence interval with the provided answer choices. $\newline$ The confidence interval is from $89\%$ to $95\%$ , which matches answer choice $(A)$ .