Exercise 39

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 $1,650. The article also states that 25% of California residents pay more than $1,800.

1. What is the Z-score that corresponds to the top 25% (or the $75^{th}$ percentile) of the standard normal distribution?

2. What is the mean insurance cost? What is the cutoff for the 75th percentile?

3. Identify the standard deviation of insurance premiums in California.