Question

Auto insurance premiums. Suppose a newspaper article states that the distribution of auto insurance premiums for residents of California is approximately normal with a mean of 1504. The article also states that 15% of California residents pay more than 1940.

1. What is the Z score that corresponds to the top 15% (or the 85thth percentile) of the standard normal distribution? Round your answer to 4 decimal places.

2. What is the mean insurance cost?

3. What is the cutoff for the 85thth percentile?

4. Identify the standard deviation of insurance premiums in LA. Round your answer to two decimal places.  Hint: Use the information from the first 3 questions in this problem and the formula for finding the z-score.

Answer 1

(A) z score = NORMSINV(alpha)

setting alpha = 1- percentile value

= 1 - 0.85

= 0.15

So, z score = NORMSINV(0.15)

= 1.0364

(B) Mean insurance cost is given as 1504

(C) Cut off for the 85th percentile is 1940 (given in question)

(D) using the formula

z =  (x-mean)/SD

or

SD = (x-mean)/z

setting the values

SD = (1940-1504)/1.0364

= 436/1.0364

= 420.69