Question
Use the mean and standsrd deviation to describe data
3, Use the mean and standard deviation to deseribe data (e.t. Empirical Rele or Chebyehev's Theorem). The follewing data are the mumber of vacation days taken by a sangle of enplkoyes during the spring quarter S8917 a. Calculate the mean, varianoe, and stamdard deviation for the data. Be sure to follow the rounding conventions -11 ,.tut ,.44 b. Based on the mean and standand deviation, is 17 an unusually high number of vacation days? Justify your answer. Heart transplant waiting times in a recent year were normally distributed, with a mean of 120 days and a standurd deviation of 27.5 days. Give a waiting time which would be considered unusual and a waiting time that would not be considered unusual (be sure to clearly indicate which is which!). Explain your answers. o Heights of men on a baseball team have a bell-shaped distribution with a mean of 175 em and a standard deviation of 8 em. Using the Empirical Rule, what is the approximate percentage of the men between: o a. 167 em and 183 cm? b. 159 cm and 191 em? Note: if you decide to change the mmbers for this exercise, be sare that the mumbers in parts a and b are exactly I, 2, or 3 standard deviations from the Grades in a class are normally distributed, with a mean of 73 and a standard deviation of 9. Using the Empirical Rule, what percent of grades are between 64 and 827 Note: if you decide to change the umbers for this exercise, be sare that the numbers in the question are exactly 1, 2, ar 3 siandard deviations from the mean o Grades in a class have a mean of 73 and a standard deviation of 9. Using Chebychev's Theorem, what can be concluded ahout the percent of grades that are between 59.5 and 86.3?
Explanation / Answer
(1)
For the data given, we have:
Mean = 8.8
Standard deviation = 4.92
Variance = 24.2
For the data value 17, the corresponding k value is:
k = (17-8.8)/4.92 = 1.67
1/k2 = 0.358
Since this value is not too small, so this value is not so unlikely.
(2)
Data given:
Mean = 2340
SD, S = 620
Given value of k = 2.25
According to Chebyshev's theorem:
No more than 1/k2 of the total distribution values lie more than k standard deviation away from the mean.
Using the data given:
k*S = 620*2.25 = 1395
1/k2 = 1/(2.25)2 = 0.197
So using chebyshev's theorem we can say that at least ((1-0.197)*100)% of the values are contained between (2340-1395) and (2340-1395).
So finally we can write:
Using chebyshev's theorem we can say that at least 80.3% of the distribution values are contained between 945 and 3735.
Hope this helps !
