Question

3. Consider the following. n = 5 measurements: 3, 3, 1, 2, 5 Calculate the sample variance, s², using the definition formula. 

Calculate the sample variance, s² using the computing formula. 

Calculate the sample standard deviation, s. (Round your answer to three decimal places.)

4. A distribution of measurements is relatively mound-shaped with a mean of 60 and a standard deviation of 13. Use this information to find the proportion of measurements in the given interval. between 47 and 73 

5. A distribution of measurements is relatively mound-shaped with a mean of 60 and a standard deviation of 14. Use this information to find the proportion of measurements in the given interval. greater than 74 

Answer 1

Question 3.

Given sample - 3,3,1,2,5

Sample size = n = 5

Definition formula for $s^2=\frac{\sum (x_i-\bar x)^2}{n-1}=\frac{\sum (x_i-2.8)^2}{4}=\frac{8.8}{4}=2.2$

Computing formula for $s^2=\frac{\sum (x_i-\bar x)^2}{n}=\frac{\sum (x_i-2.8)^2}{5}=\frac{8.8}{5}=1.76$

Sample standard deviation =

S Στη - )2 η –1 V2.2 = 1.483

Question 4.

Let X denote the measurement

X follows mount shaped distribution ( Normal distribution) with mean
09
and standard deviation $\sigma=13$

follows Standard normal distribution

- Z

$P[47<X<73]=P[\frac{47-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{73-\mu}{\sigma}]=P[-1<Z<1]$

Proportion of measurements in the interval (47,73) is 68.26%

Question 5.

Let X denote the measurement

X follows mount shaped distribution ( Normal distribution) with mean
09
and standard deviation $\sigma=14$

follows Standard normal distribution

- Z

$P[X>74]=P[\frac{X-\mu}{\sigma}<\frac{74-\mu}{\sigma}]=P[Z<1]=0.8413$

Proportion of measurements greater than 74 is 68.26%

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