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 \({{ params.description.num1 }}\) dollar. The article also states that \({{params.description.top_percent}}\)% of California residents pay more than \({{ params.description.num3 }}\) dollar.

Part 1

What is the Z-score that corresponds to the top \({{params.description.top_percent}}\)% (or the \({{params.description.percentile}}^{th}\) percentile) of the standard normal distribution?

Part 2

What is the mean insurance cost?

Part 3

What is the cutoff for the \({{params.description.percentile}}^{th}\) percentile?

Part 4

Identify the standard deviation of insurance premiums in California.

Attribution

Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.