Question 1200576
mean is 25.5 mpg
standard deviation is 2.25 mpg
critical z-score for 98% probability = plus or minus z = 2.326347877.
z = (x - m) / s
z is the z-score
x is the raw score
m is the poulation mean
s is the population standard deviation
to solve for x, the formula becomes:
x = z * s + m
when z = 2.326347877 and m = 25.5 and s = 2.25, the formula becomes:
x = -2.326347877 * 2.25 + 25.5 = 20.26571728 on the low side.
x = 2.326347877 * 2.25 + 25.5 = 30.734202672 on the high side.
rounds as required.
this is what it looks like, using the calculator at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>
<img src = "http://theo.x10hosting.com/2023/022501.jpg">