Question

An insurance company checks police records on 553 accidents selected at random and notes that teenagers...

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.)

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%)

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