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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 1673. The article also states that 15% of California residents pay more than 1930.

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

b)What is the mean insurance cost?

c)What is the cutoff for the 85th percentile?

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

math   Statistics-And-Probability   
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Answer #1

Given that,

mean = = 1673

standard deviation = =

(a)

P(Z < 1.04) = 0.85

z = 1.04

(b)

= 1673

(c)

x = 1930

(c)

1.04 = (1930 - 1673) /

= 257 / 1.04 = 247.12

the standard deviation of insurance premiums in LA = 247.12

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