131-MATH2DNOTES.docx - 4.6 EXERCISES 4.11 Auto insurance...

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4.6. EXERCISES4.11 Auto insurance premiums. Suppose a newspaper article states that the distribution of autoinsurance 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.(a)What is the Z-score that corresponds to the top 25% (or the 75thpercentile) of the standard normal distribution?(b)What is the mean insurance cost? What is the cuto for the 75th percentile?(c)Identify the standard deviation of insurance premiums in LA.4.12 Speeding on the I-5, Part I. The distribution of passenger vehicle speeds traveling on theInterstate 5 Freeway (I-5) in California is nearly normal with a mean of 72.6 miles/hour and astandard deviation of 4.78 miles/hour.39(a)What percent of passenger vehicles travel slower than 80 miles/hour?(b)What percent of passenger vehicles travel between 60 and 80 miles/hour?(c)How fast do the fastest 5% of passenger vehicles travel?(d)The speed limit on this stretch of the I-5 is 70 miles/hour. Approximate what percentage of the passenger vehicles travel above the speed limit on this stretch of the I-5.

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