Question

Every year, 1,000 engineers compete in a sports car road race. The mean (average) finishing time is 55 minutes, with a standard deviation of 10 minutes. Justin and Cindy completed the race in 61 and 51 minutes, respectively. Barry and Lisa had finishing times with Z-scores of -0.3 and 0.7, respectively. Since the Z-score is the number of standard deviations above the mean, then the lowest Z-score corresponds to the fastest car. List the drivers, fastest to the slowest, based on their Z-scores.

Answer 1

the PDF of normal distribution is 1/σ * V2n * e ^-(x-u)^2/ 2on2 standard normal distribution is a normal distribution with a, mean of 0, standard deviation of 1 equation of the normal curve is (Z)-x u sd N(0,1) Justin Z score calculation mean (u) 55 Standard Deviation ( sd )= 10 P(X = 61) = (61-55)/10 Justin Z score 0.6 Cindy Z score calculation P(X 51)(51-55)/10 Barry and Lisa had finishing times with Z-scores of -0.3 and 0.7 arrange the Drivers fastest to the slowest based on Z score, 0.7, 0.6, -0.3, -0.4 Lisa, Justin, Barry and Lisa