Question

6. During the lunch hour rush, the number of vehicles

passing through the drive-thru at the Wendy's at
Appleby Line and Dundas has been determined to be
normally distributed with a mean of 38 vehicles and
a standard deviation of 5.7. What is the probability
that on a given day, exactly 35 vehicles pass through
the drive thru during the lunch hour rush?

Answer 1

Explanation:

To find the probability that exactly 35 vehicles pass through the drive-thru during the lunch hour rush on a given day, we can use the probability density function of the normal distribution. In this case, the mean is 38 and the standard deviation is 5.7.

The probability of a specific value x in a normal distribution is given by the formula:

P(x) = (1/(σ * √(2π)) * e^((-1/2) * ((x - μ)^2 / σ^2))

Where x is the specific value we are trying to find the probability of, μ is the mean, and σ is the standard deviation.

plugging in the given values, we get:

P(35) = (1/(5.7 * √(2π)) * e^((-1/2) * ((35 - 38)^2 / 5.7^2))

The result is very close to zero, the probability of exactly 35 vehicles passing through the drive-thru during the lunch hour rush is very low, almost impossible.