Question

The average speed of vehicles traveling on a stretch of highway is 67 miles per hour with a standard deviation of 3.5 miles per hour. A vehicle is selected at random. What is the probability that it is violating the speed limit of 70 miles per hour? Assume the speeds are normally distributed and are represented by the variable X.Hint: Convert the normal distribution X to Standard normal using Z formula Z=(X-μ)/σ and then look the Z-values from the table and then find the probability.Please help a 61 woman trying to do exercises to get GED in desperate need of help I don’t know how to do it step-by-step inserting numbers into the formula please help

Answer 1

From the question given, we will be solving for:

P(X > 70)

Normal distribution:

μ = 67

σ = 3.5

Let's convert to standard normal usung:

z = x - μ

σ

z = 70 - (67) = 0.857143

3.5

z = 0.86

P(Z > 0.86) = Area to the right of 0.86

P(X > 70) = P(Z > 0.86) = 1 - P(Z < 0.86) = 1 - 0.8051

= 0.1949 (From standard normal table

Hence, the probability that is violating the 70 mile per hour speed limit is: 0.1949

P(X > 70) = 0.1949