Suppose the total snowfalls per year in a city are normally distributed. if the population standard deviation is 13 inches, what minimum sample size is needed to be 95% confident that the sample mean is within 4 inches of the true population mean?

41

Step-by-step explanation:

Given : Significance level :

Critical value :

Margin of error :

Standard deviation:

The formula to find the sample size :

Then, we have

Hence, the minimum sample size needed= 41.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.