Question

b. the manufacturers suggested retail price (msrp) for this car model is at the 98th percentile of the distribution of asking price. find the value of the msrp.
35,987 + (2.05×5007.50) = 35,987 + 10,265.38 =
46,252

Explanation:

Step1: Identify the formula components

We have a formula for finding a value at a percentile in a normal distribution (assuming), which is \( x = \mu + z\sigma \), where \( \mu = 35987 \), \( z = 2.05 \) (z - score for 98th percentile), and \( \sigma = 5007.50 \).

Step2: Calculate the product of z and σ

First, calculate \( z\times\sigma = 2.05\times5007.50 \). Let's compute that: \( 2.05\times5007.50 = 10265.375 \approx 10265.38 \)

Step3: Add the mean (μ) to the result

Now, add this to the mean \( \mu = 35987 \). So, \( 35987+ 10265.38 = 46252.38 \approx 46252 \) (or as in the given, 46252 when rounded appropriately, and the circled value is 46,252 which matches our calculation).

Answer:

The value of the MSRP is \( \boldsymbol{46252} \) (or 46,252 as in the hand - written solution).