During one season of racing at the Talladega Superspeedway,

Question

During one season of racing at the Talladega Superspeedway, the mean speed of the cars racing there was found to be 158.9 mph with a standard deviation of 6.7 mph. What speed represents the 30th percentile for speeds of race cars at Talladega? Assume that the racing speeds are normally distributed.

Answer 1

Let x represent the 30th percentile speed for Normal X with parameters mean=158.9, stdev=6.7

P(X<z) = 0.3 <-- 30th percentile

z = -0.525  <--- from the normal table , doing a reverse lookup 

 

However, this value is the z-score. To convert it back to scale,

-0.525 = (x - 158.9)/6.7

X = 155.3285