Question

An insurance company checks police records on 553 accidents selected at random and notes that teenagers were at the wheel in 85 of them. ​a) Construct the​ 95% confidence interval for the percentage of all auto accidents that involve teenage drivers. ​95% CIequalsleft parenthesis nothing % comma nothing % right parenthesis ​(Round to one decimal place as​ needed.)

Answer 1

total number of accidents = 553, this is the sample size(n)

number of teenagers = 85

So, the proportion = 85/553 = 0.154

Normal standard deviation gives us the critical z score 1.96 for 95% confidence interval

Using the formula, Confidence interval =

putting the given values in the above formula, we get

Confidence interval =

Multiplying by 100 to get the required percentages

0.124*100 = 12.4 and 0.184*100 = 18.4

So, the required confidence interval is (12.4%, 18.4%)