Radon is a naturally occurring gas and is the second leading cause of lung cancer in the United States. It comes from the natural breakdown of uranium in the soil and enters buildings through cracks and other holes in the foundations. Found throughout the United States, levels vary considerably from state to state. Several methods can reduce the levels of radon in your home, and the Environmental Protection Agency ecommends using one of these if the measured level in your home is above 4 picocuries per liter. Four readings from Franklin County, Ohio, where the county average is 9.32 picocuries per liter, were 5.2, 13.8, 8.6, and 16.8. Required:
a. Find the mean step-by-step.
b. Find the standard deviation step-by-step.

a) mean =  11.1

b) Standard Deviation = 5.191

Step-by-step explanation:

Given the data in the question;

x = 5.2, 13.8, 8.6, and 16.8

sample n = 4

so;

            x            ( x - mean)²

          5.2             34.81

          13.8            7.29

          8.6             6.25

          16.8            32.49

∑        44.4            80.84

a) Mean

Mean = total sum of the sample divided by the sample size

mean = ∑x / n

we substitute

mean = 44.4 / 4

mean =  11.1

b)

Standard Deviation is the Square root of variance;

Variance = ∑(x-mean)² / n - 1

we substitute from the above table

Variance =  80.81 / 4 - 1

Variance =  80.81 / 3

Variance =  26.94667

now since Standard Deviation is the Square root of variance;

Standard Deviation = √Variance

Standard Deviation = √26.94667

Standard Deviation = 5.191

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get