Question

A medical laboratory tested 8 samples of human blood for acidity on the pH​ scale, with the results below.

7.4  

7.4   

7.1  

7.5   

7.3  

7.3   

7.6  

7.2

a. Find the mean and standard deviation.

b. What percentage of the data is within

2

standard

deviations

of the​ mean?

Answer 1

A medical laboratory tested 8 samples of human blood for acidity on the pH scale.

Observation table -

	x	(x - x_bar)^2
	7.4	0.0025
	7.4	0.0025
	7.1	0.0625
	7.5	0.0225
	7.3	0.0025
	7.3	0.0025
	7.6	0.0625
	7.2	0.0225
Total	58.8	0.18

a) -

So,

b) -

95% of the data lies within two standard deviations of the mean i.e. 95% lies within the range [M - 2SD, M + 2SD].

So, Approximately 95% of the data lies within between 2 standard deviations of mean is -

[M - 2SD, M + 2SD] = [7.35 - 2(0.15), 7.35 + 2(0.15)] = [7.05, 7.65]

Hence, Approximately 95% of the data lies within between 2 standard deviations of mean is between 7.05 & 7.65.