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%)**

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