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 10.0 mph. What speed represents the 33rd percentile for speeds of race cars at Talladega? Assume that the racing speeds are normally distributed.

Answer 1

154.5 mph

Step-by-step explanation:

mean: 158.9 mph, SD: 10.0 mph

Need to convert the mean and SD into normal distribution.

We know P(X<z) = 0.33

From the normal distribution table, P(X<z) = 0.33, z value is -0.44

P(X< -0.44) = 0.33

we know
`(x-mean)/(SD) = Z`

`(x-158.9)/(10) = -0.44\\x=154.5`