Auto insurance premiums. Suppose a newspaper article states that the distributio

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 1536. The article also states that 25% of California residents pay more than 1950.

1. What is the Z score that corresponds to the top 25% (or the 75th

percentile) of the standard normal distribution? Round your answer to three decimal places.

2. What is the mean insurance cost?

3. What is the cutoff for the 75th percentile?

4. Identify the standard deviation of insurance premiums in LA. Round your answer to two decimal places.

Explanation / Answer

1)z score  that corresponds to the top 25% =0.674

2)

mean insuarance cost =1536

3)

cutoff for the 75th percentile =1950

4)

standard deviation of insurance premiums =(X-mean)/z score =(1950-1536)/0.674=614.24

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