Question

In a large? city, 65 ?% of people pass the? drivers' road test. Suppose that every? day, 300 people independently take the test. In a large? city,65?% of people pass the? drivers' road test. Suppose that every? day, 300 people independently take the test.

After a great many? days, according to the Empirical? Rule, on about? 95% of these? days, the number of people passing will be as low as? _____ and as high as? _____. (Hint: Find two standard deviations below and two standard deviations above the? mean.)

Answer 1

Let X denotes the number of people passing out of 300 people who independently take the test everyday.

X ~ Binomial(300, 0.65)

The probability mass function of X is

$P(X=x) = \binom{300}{x}*0.65^x*(1-0.65)^{300-x},x=0,1,2,...,300$

Here

Mean

Standard deviation $sd(X) = \sqrt{300*0.65*(1-0.65)} = 8.26136$

Mean - (2*sd)  

Mean + (2*sd)