Answer each question with steps on how to do them

Question

The speeds of vehicles passing through a construction zone are normally distributed with a mean of 47 miles per hour and standard deviation of 3 miles per hour.

Part A

If 45% of vehicles passing through this construction zone exceed the speed limit, what is the speed limit at this construction zone?

(Rounding the speed limit to 3 decimal places if possible)

 miles per hours

Part B

About middle 30% of vehicles passing through this construction zone travel between  and  miles per hours .

(Rounding the speed limit to 3 decimal places if possible)

Part C

What percent of vehicles passing through this construction zone travel at between 42 and 49 miles per hour?

(Rounding the percentage to 2 decimal places if possible)

 %

Answer 1

Greetings,

Set up your bell curve graph and place the mean (47mph) and standard deviation (3mph).

Part A:

Here you are given a percentage, so we will use the Invnorm (Inverse Normal) distribution, which a is the area, u(mu) is the mean, o(sigma) is the standard deviation. You may do it by hand and/or other calculation methods.

Invnorm (a,u,o) = (.45, 47,3) = 46.623 mph

Part B:

In this section, we will split the bell curve into segments of the middle 30%, which will leave 70% for the remaining areas. On the left of the middle 30% will be 35% and the right will be 35%.

Left side: Invnorm (a, u, o) = (.35,47,3) = 45.844 mph

Right side: Invnorm (a, u o) = (.65, 47, 3) = 48.156 mph

**Note here that we will add the left 35% and middle 30% to obtain 65% and/or you may use 100% and subtract the right 35% to obtain 65%. This is foresight for other problems you may encounter with different percentage values.

Part C:

In this section, we will use the Normalcdf function, which u (mu) is the mean, o (sigma) is the standard deviation, L is your lower (left) boundary, U is your (right) boundary.

Now we need to find the probability (percentage), P(42 < x < 49).

Normalcdf (u, o, L, U): ( 47, 3, 42, 49) = 0.69972 => approximately = 69.97%

If you need more help with doing it by hand and/or calculator, consider scheduling a session with me.