Radon is a naturally occurring gas and is the second leading cause of lung cance
ID: 2731721 • Letter: R
Question
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 recommends using one of these if the measured level in your home is above 4 picocuries per liter. Four readings from a county in the state of Ohio, where the county average is 8.4 picocuries per liter, were 5.4, 13.6, 7.6, and 16.2.
(a) Find the mean step-by-step. That is, find the sum of the 4 observations and divide by 4. (Enter your answers to one decimal place.)
(b) Find the standard deviation step-by-step. That is, find the deviations of each observation from the mean, square the deviations, then obtain the variance and the standard deviation. (Round your answers to two decimal places.)
xi
xi x
(xi x)2
(c) Now enter the data into your calculator and use the mean and standard deviation buttons to obtain x and s. (Round your answers to two decimal places.)
Do the results agree with your hand calculations?
Yes
No
sum picocuries mean picocuriesExplanation / Answer
Answers (a) Sum= 5.4 + 13.6+ 7.6+16.2 = 42.8 picocuries
Mean = Sum / 4 = 42.8/4 = 10.7(x) picocuries
Now lets find the Variance S^2
Answer (b)= xi 5.4 13.6 7.6 16.2
xi - x (5.4-10.7)^2 + (13.6-10.7)^2 + (7.6-10.7)^2 + (16.2-10.7)^ 2
( xi - x)^2 (5.4-10.7)^2 + (13.6-10.7)^2 + (7.6-10.7)^2 + (16.2-10.7)^ 2 4 - 1
s^2 28.90 + 8.41 + 9.61 + 30.25 / 3 = 25.7233
Standard Deviation = s = under root of 25.7233 = 5.0718 picocuries
(c) x = 10.7
s = 25.72 picocuries
Yes the results agree with the hand calculation as well .
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