Math / Data & Statistics

QuestionCoffee: The National Coffee Association reported that $63 \%$ of U.S. adults drink coffee daily. A random sample of 250 U.S. adults is selected. Round your answers to at least four decimal places as needed.
Part 1 of 2 (a) Find the probability that more than $64 \%$ of the sampled adults drink coffee daily.
The probability that more than $64 \%$ of the sampled adults drink coffee daily is 0.3721 .
Part: $1 / 2$
Part 2 of 2 (b) Find the probability that the proportion of the sampled adults who drink coffee daily is between 0.62 and 0.68 .
The probability that the proportion of the sampled adults who drink coffee daily is between 0.62 and 0.68 is $\square$ .

Studdy Solution
Find the probability that the proportion is between 0.62 and 0.68 using the standard normal distribution:
$P(0.62 < \hat{p} < 0.68) = P(-0.3268 < Z < 1.6340)$
Using standard normal distribution tables or a calculator, find:
$P(Z < 1.6340) \approx 0.9484$ $P(Z < -0.3268) \approx 0.3729$
Calculate the probability:
$P(-0.3268 < Z < 1.6340) = 0.9484 - 0.3729 = 0.5755$
The probability that the proportion of the sampled adults who drink coffee daily is between 0.62 and 0.68 is:
$\boxed{0.5755}$

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