Question

Refer to speeds at which cars pass through a checkpoint on the highway. Assume the speeds are normally distributed with a population mean of 61 miles per hour and a population standard deviation of 4 miles per hour. Calculate the probability that the next car passing will be travelling more than 58 miles per hour.

Answer 1

Mean = 61 miles per hour

Standard deviation = 4 miles per hour

Value that is being standardized= 58 miles per hour

We need to find the probability

P (Z > (58-61)/4)

or P (Z > -3/4)

or P (Z > -0.75)

P (Z > -0.75) has the same value as P (Z < 0.75). This is because of the symmetry of the standard normal distribution curve.

From standard normal distribution table, P (Z < 0.75) = 0.22663

Thus, P(Z > -0.75) = 0.22663

Hence probability that the next car passing will be travelling more than 58 miles per hour is 0.22663