Question

In: Statistics and Probability

Suppose a newspaper article states that the distribution of auto insurance premiums for residents of California...

Suppose a newspaper article states that the distribution of auto insurance premiums for residents of California is approximately normal with a mean of 1502. The article also states that 25% of California residents pay more than 1875.

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

- Please input your calculator functions. For example for normalcdf please show me all the values you used. Thanks!

Solutions

Expert Solution

Suppose a newspaper article states that the distribution of auto insurance premiums for residents of California is approximately normal with a mean of 1502. The article also states that 25% of California residents pay more than 1875.

What is the Z score that corresponds to the top 25% (or the 75thth percentile) of the standard normal distribution? Round your answer to 4 decimal places.

z=0.6745

Excel function used to get z value: =NORM.S.INV(0.75)

What is the mean insurance cost? 1502

3. What is the cutoff for the 75thth percentile

cutoff for the 75thth percentile=1875

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

we know that z = (x-µ)/σ

0.6745 = (1875-1502)/ σ

σ = (1875-1502)/ 0.6745

=553.0022239

=553.00 ( two decimals)

orchestra answered 2 years ago
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