EXAMPLE 41Finding the -values that mark the boundaries of the middle 95% of -values

Edmunds.com reported that the average amount that people were paying for a 2015 Toyota Camry XLE was $28,720. Let , and assume that price follows a normal distribution with and . Find the prices that separate the middle 95% of 2015 Toyota Camry XLE prices from the bottom 2.5% and the top 2.5%.

Solution

  • Step 1 Determine , , and , and draw the normal curve for .

    Let , , and . The middle 95% of prices are between and , as shown in Figure 53.

  • Step 2 Find the -values corresponding to the desired area.

    The area to the left of equals 0.025, and the area to the left of equals 0.975. Looking up area 0.025 on the inside of the table gives us . Looking up area 0.975 on the inside of the table gives us .

    image
    Figure 6.55: FIGURE 53 and mark the middle 95% of Camry XLE prices.

  • Step 3 Transform using the formula .

    We calculate

    The prices that separate the middle 95% of 2015 Toyota Camry XLE prices from the bottom 2.5% of prices and the top 2.5% of prices are $26,760 and $30,680.

NOW YOU CAN DO

Exercises 23–26.