Question

A survey in September 2020 of 1000 gas stations found that the price charged for a gallon of regular gas could be closely approximated by a normal distribution with a mean of $3.53 and a standard deviation of $0.20.
Draw the normal distribution with these numbers.
a. How many stations charge over $3.93?
b. How many of the stations charge between $3.13 and $3.93 for a gallon?
c. How many stations charge less than $3.33?

Answer 1

Basically given normal distribution we have to draw the bell curve with standard deviations which should look like(picture below) so draw something like that with center number being mean (3.53) and each positive standard deviation(SD) being + 0.2:
Ex 1 SD is 3.73, 2SD is 3.93, -1SD is 3.33

Now to solve the questions
A. If we know there’s 1000 gas stations and 3.93 is just 2 SD we can just refer to the picture below.
Basically because we’re finding the amount of values that are greater than that it should be percentage to the right of 2 SD. Which is 2.2% or 0.022 Then multiply that by the number of gas station.
So 0.022 * 1000 = 22.
B. This is basically the values between -2SD and 2 SD which is the percentage between them. Add 13.6 *2 + 34.1*2 = 95.2% or 0.952
Now multiply by 1000 * 0.952=952 gas stations.
C. For this one we just find percentage to the left of -1 SD or simpler just subtract half(the right half) and the percentage in 1 SD from 1 to find the remainder which is the value left of -1SD.
1-0.5 - 0.341 = 0.159
Now multiply by 1000 * 0.159 = 159 stations.

Hopefully this helps.