A random sample of international flights in 2013 showed that 79% of the flights arrived within 15 minutes of their scheduled arrival time, and this estimate had a margin of error of 3% at a 95% confidence level. Which of the following conclusions is best? Choose 1 answer: A Exactly 79% arrived within 15 minutes of their scheduled times. (B) Exactly 76% arrived within 15 minutes of their scheduled times. (c) Between 76% and 82% arrived within 15 minutes of their scheduled times. (D) Between 92% and 98% arrived within 15 minutes of their scheduled times.

Problem statement: The problem states that 79% of the flights arrived within 15 minutes of their scheduled arrival time with a margin of error of 3% at a 95% confidence level. To find the range, we need to add and subtract the margin of error from the estimated percentage.Calculate lower bound: Calculate the lower bound of the confidence interval by subtracting the margin of error from the estimated percentage. Lower bound = Estimated percentage - Margin of error Lower bound = 79% - 3% Lower bound = 76%Calculate upper bound: Calculate the upper bound of the confidence interval by adding the margin of error to the estimated percentage. Upper bound = Estimated percentage + Margin of error Upper bound = 79% + 3% Upper bound = 82%Determine range: Now we have the range for the confidence interval. The range is from 76% to 82%.Compare with options: Compare the range with the given options to determine the best conclusion. Option (C) states ＂Between 76% and 82% arrived within 15 minutes of their scheduled times,＂ which matches our calculated range.

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A random sample of international flights in $2013$ showed that $79 \%$ of the flights arrived within $15$ minutes of their scheduled arrival time, and this estimate had a margin of error of $3 \%$ at a $95 \%$ confidence level. Which of the following conclusions is best? $\newline$ Choose $1$ answer: $\newline$ (A) Exactly $79 \%$ arrived within $15$ minutes of their scheduled times. $\newline$ (B) Exactly $76 \%$ arrived within $15$ minutes of their scheduled times. $\newline$ (C) Between $76 \%$ and $82 \%$ arrived within $15$ minutes of their scheduled times. $\newline$ (D) Between $92 \%$ and $98 \%$ arrived within $15$ minutes of their scheduled times.

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Math Problems

Algebra 2

Interpret confidence intervals for population means

Full solution

Q. A random sample of international flights in

2013

showed that

79 \%

of the flights arrived within

15

minutes of their scheduled arrival time, and this estimate had a margin of error of

3 \%

at a

95 \%

confidence level. Which of the following conclusions is best?

\newline

Choose

1

answer:

\newline

(A) Exactly

79 \%

arrived within

15

minutes of their scheduled times.

\newline

(B) Exactly

76 \%

arrived within

15

minutes of their scheduled times.

\newline

76 \%

and

82 \%

arrived within

15

minutes of their scheduled times.

\newline

(D) Between

92 \%

and

98 \%

arrived within

15

minutes of their scheduled times.

Problem statement: The problem states that $79\%$ of the flights arrived within $15$ minutes of their scheduled arrival time with a margin of error of $3\%$ at a $95\%$ confidence level. To find the range, we need to add and subtract the margin of error from the estimated percentage.
Calculate lower bound: Calculate the lower bound of the confidence interval by subtracting the margin of error from the estimated percentage. $\newline$ Lower bound = Estimated percentage - Margin of error $\newline$ Lower bound = $79\% - 3\%$ $\newline$ Lower bound = $76\%$
Calculate upper bound: Calculate the upper bound of the confidence interval by adding the margin of error to the estimated percentage. $\newline$ Upper bound = Estimated percentage + Margin of error $\newline$ Upper bound = $79\% + 3\%$ $\newline$ Upper bound = $82\%$
Determine range: Now we have the range for the confidence interval. $\newline$ The range is from $76\%$ to $82\%$ .
Compare with options: Compare the range with the given options to determine the best conclusion. $\newline$ Option (C) states ＂Between $76\%$ and $82\%$ arrived within $15$ minutes of their scheduled times,＂ which matches our calculated range.