Question

Question 4: The speed on a roadway segment has a population mean of 60 mph and population standard deviation of 10 mph. You collect 100 speed samples every day and determine the average travel speed. Determine the probability that the average travel speed will be higher than 63 mph? (4 points) n -1 tix yn

Answer 1

Mean = $\mu$ = 60

Standard deviation = $\sigma$ = 10

Sample size = n = 100

We have to find P( $\bar{x}$ > 63)

For finding this probability we have to find z score.

$z =\frac{\bar{x}-\mu }{\sigma /\sqrt{n}}$

$z =\frac{63-60 }{10 /\sqrt{100}}=\frac{3}{1}=3$

That is we have to find P(Z > 3)

P(Z > 3) = 1 - P(Z < 3) = 1 - 0.9987 = 0.0013