S.Q.2.4

Recognize a sampling distribution is the distribution of a sample statistic (e.g., sample mean, sample proportion) obtained from repeated samples.

Example Problems
A credit union claims that 35% of its roughly 70,000 cardholders use automatic payments. A financial blogger takes a simple random sample of 280 cardholders and asks about autopay.

Assuming the credit union's claim is correct, what is the probability that the sample result is within
4 percentage points of the 35% claim?
Round your answer to the nearest hundredth.
A newsletter team claims that 47% of its more than 200,000 subscribers opened the most recent email. An auditor takes a simple random sample of 160 subscribers and checks whether they opened it.

Assuming the team's
47% claim is correct, what is the approximate probability that more than 50% of the sample opened the email?
Round your answer to the nearest hundredth.
A taco stand tops a certain taco with 5 slices of jalapeño. The slices have a mean mass of grams and a standard deviation of grams. We can assume that the masses of the slices are independent from each other. Let be the total mass of the jalapeño slices on a randomly chosen taco.

Find the
mean of T, .
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