A surprising fact: only 56% of all teens use a password on their mobile device. If a poll chooses a simple random sample of 1000 teens and asks if they use a password on their mobile device, the percent who say "Yes" will vary if the sample is repeated. In fact, the percent "Yes" in many samples will follow a normal distribution with mean 56% and standard deviation 1.6%.
Which of these ranges of outcomes contains 95 percent of all the results of a large number of polls of 1,000 teens?
A) 56 to 100 percent
B) 54.4 to 57.6 percent
C) 52.8 to 59.2 percent
D) 51.2 to 60.8 percent

Question

Quizplus · Accepted Answer

We can use the normal distribution formula to find the range of outcomes that contains 95% of all the results:

range = mean ± 1.96 * standard deviation

Plugging in the given values, we get:

range = 56 ± 1.96 * 1.6

range = 52.8 to 59.2 percent

Therefore, Choice C (52.8 to 59.2 percent) contains 95% of all the results of a large number of polls of 1,000 teens.

A Surprising Fact: Only 56% of All Teens Use a Password