Statistics: Normal Distribution and Confidence

Normal distribution, standard deviation, z-scores, and interpreting confidence intervals and margin of error.

8 questions, free, marked as you go with a worked explanation on every one.

What this covers

Scores on a test are normally distributed with a mean of 70 and a standard deviation of 8. A student scores 82. What is that student's z-score?
A machine fills bags with a mean mass of 500 g and a standard deviation of 10 g, normally distributed. Using the 68-95-99.7 rule, what percentage of bags have a mass between 480 g and 520 g?
Light bulbs have a mean life of 1 200 hours with a standard deviation of 100 hours, normally distributed. The manufacturer offers a refund on any bulb that fails before 1 000 hours. Using the 68-95-99.7 rule, what percentage of bulbs should qualify for a refund?
A poll reports that 52% of voters support a policy, with a margin of error of 3 percentage points, 19 times out of 20. What does this mean?
Two students compare results. Priya scored 78 on a test with mean 70 and standard deviation 4. Dan scored 84 on a different test with mean 75 and standard deviation 6. Who performed better relative to their class?
A survey of voters reports 46% support with a margin of error of 4 percentage points. What is the upper bound of the confidence interval, as a percent?
Which of the following are true about a normal distribution?
A polling company wants to reduce its margin of error. It currently surveys 400 people and reports a margin of error of 5 percentage points. Margin of error is inversely proportional to the square root of the sample size. How many people must it survey to halve the margin of error to 2.5 percentage points?