(9) One of a hotel’s largest expenditures is laundry. Hotels look for the sturdi
ID: 3244051 • Letter: #
Question
(9) One of a hotel’s largest expenditures is laundry. Hotels look for the sturdiest washing machines with the longest working life. Hart Hotel buys washing machines from two vendors—SpeedCleen and Sparkle. Statistics on the working life of both vendors’ machines are shown below:
SpeedCleen
Sparkle
Mean
48.2 months
46.4 months
Median
43.8 months
46.4 months
Standard Deviation
3.1 months
4.2 months
(a)Which washer life is right-skewed?
SpeedCleen, because it has a smaller standard deviation.
Sparkle, because its mean and median are equal.
Sparkle, because it has a bigger standard deviation.
SpeedCleen, because its mean exceeds its median.
(b)According to the Empirical Rule, approximately 95% of all Sparkle machines
will last for between:
38 and 54.8 months.
42 and 54.4 months
42.2 and 50.6 months
46.4 and 48.2 months
(c) According to the Chebyshev Rule, at least 75% of all SpeedCleen machines will
last for between:
38 and 54.8 months
43.8 and 46.4 months
45.1 and 51.3 months
42 and 54.4 months
SpeedCleen
Sparkle
Mean
48.2 months
46.4 months
Median
43.8 months
46.4 months
Standard Deviation
3.1 months
4.2 months
Explanation / Answer
A) for right skewed, mean is always greater than median.
So the correct Option is Option-D)
B) according to empirical rule mean +/- 2*standard deviation covers 95% of the area.
So, mean + 2*SD = 46.4 + 2 * 4.2
= 46.4 + 8.4
= 38 , 54.8
Option-A)
C) according to chebyshev rule, mean + k*SD covers (1 - 1/k2)
So, 1 - 1/k2 = 0.75
Or, k = 2
So, mean + 2*sd = 48.2 + 2*3.1
= 48.2 + 6.2
= 42 , 54.4
Option-D
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.