QuestionA city inspector found that $41.1\%$ of 500 buildings met readiness conditions with a margin of error of $\pm 5\%$ . What must be true?

Studdy Solution

STEP 1

Assumptions1. The sample size is500 commercial buildings. . The percentage of buildings that met the readiness conditions in all areas is41.1%.
3. The margin of error associated with the survey is ±5%.

STEP 2

The margin of error means that the actual percentage of buildings that met the readiness conditions in all areas could be as low as41.1% -5% or as high as41.1% +5%.

STEP 3

Calculate the lower bound of the percentage of buildings that met the readiness conditions in all areas.
$Lower\, bound =41.1\% -5\%$

STEP 4

Calculate the value of the lower bound.
$Lower\, bound =41.1\% -\% =36.1\%$

STEP 5

Calculate the upper bound of the percentage of buildings that met the readiness conditions in all areas.
$Upper\, bound =41.1\% +5\%$

STEP 6

Calculate the value of the upper bound.
$Upper\, bound =41.1\% +5\% =46.1\%$

STEP 7

Based on the calculated lower and upper bounds, we can evaluate the statements given in the problem.
A) The percentage of commercial buildings in the city that met the readiness conditions was likely to be greater than $36.1 \%$ . This statement is true because the lower bound of the percentage is36.1%.
B) The percentage of commercial buildings in the city that met the readiness conditions in all areas was $41.1 \%$ . This statement is not necessarily true because the actual percentage could be anywhere between the lower bound (36.1%) and the upper bound (46.1%).
C) The percentage of commercial buildings in the city that met the readiness conditions in all areas was at most $46.1 \%$ . This statement is true because the upper bound of the percentage is46.1%.
) The number of commercial buildings in the city that met the readiness conditions in all areas was greater than the number that did not meet the readiness conditions in all areas. This statement is not necessarily true because the percentage that met the readiness conditions (41.1%) is less than the percentage that did not meet the readiness conditions (58.9%).
Based on the above evaluations, the statements A and C must be true based on the results of the study.

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QuestionA city inspector found that $41.1\%$ of 500 buildings met readiness conditions with a margin of error of $\pm 5\%$ . What must be true?

Studdy Solution

STEP 1

Assumptions1. The sample size is500 commercial buildings. . The percentage of buildings that met the readiness conditions in all areas is41.1%.
3. The margin of error associated with the survey is ±5%.

STEP 2

The margin of error means that the actual percentage of buildings that met the readiness conditions in all areas could be as low as41.1% -5% or as high as41.1% +5%.

STEP 3

Calculate the lower bound of the percentage of buildings that met the readiness conditions in all areas.
$Lower\, bound =41.1\% -5\%$

STEP 4

Calculate the value of the lower bound.
$Lower\, bound =41.1\% -\% =36.1\%$

STEP 5

Calculate the upper bound of the percentage of buildings that met the readiness conditions in all areas.
$Upper\, bound =41.1\% +5\%$

STEP 6

Calculate the value of the upper bound.
$Upper\, bound =41.1\% +5\% =46.1\%$

STEP 7

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QuestionA city inspector found that 41.1%41.1\%41.1% of 500 buildings met readiness conditions with a margin of error of ±5%\pm 5\%±5%. What must be true?

Studdy Solution

STEP 1

Assumptions1. The sample size is500 commercial buildings. . The percentage of buildings that met the readiness conditions in all areas is41.1%.3. The margin of error associated with the survey is ±5%.

STEP 2

The margin of error means that the actual percentage of buildings that met the readiness conditions in all areas could be as low as41.1% -5% or as high as41.1% +5%.

STEP 3

Calculate the lower bound of the percentage of buildings that met the readiness conditions in all areas.Lower bound=41.1%−5%Lower\, bound =41.1\% -5\%Lowerbound=41.1%−5%

STEP 4

Calculate the value of the lower bound.Lower bound=41.1%−%=36.1%Lower\, bound =41.1\% -\% =36.1\%Lowerbound=41.1%−%=36.1%

STEP 5

Calculate the upper bound of the percentage of buildings that met the readiness conditions in all areas.Upper bound=41.1%+5%Upper\, bound =41.1\% +5\%Upperbound=41.1%+5%

STEP 6

Calculate the value of the upper bound.Upper bound=41.1%+5%=46.1%Upper\, bound =41.1\% +5\% =46.1\%Upperbound=41.1%+5%=46.1%

STEP 7

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QuestionA city inspector found that $41.1\%$ of 500 buildings met readiness conditions with a margin of error of $\pm 5\%$ . What must be true?

Assumptions1. The sample size is500 commercial buildings. . The percentage of buildings that met the readiness conditions in all areas is41.1%.
3. The margin of error associated with the survey is ±5%.

Calculate the lower bound of the percentage of buildings that met the readiness conditions in all areas.
$Lower\, bound =41.1\% -5\%$

Calculate the value of the lower bound.
$Lower\, bound =41.1\% -\% =36.1\%$

Calculate the upper bound of the percentage of buildings that met the readiness conditions in all areas.
$Upper\, bound =41.1\% +5\%$

Calculate the value of the upper bound.
$Upper\, bound =41.1\% +5\% =46.1\%$