Question 3 The mean number of liters of beer taken per custo

The mean number of liters of beer taken per customers at The Kilroy\'s Pub is 9.5 liters with a standard deviation of 0.75 liters. The median number of liters of beer consumed is 10.0 liters. The arithmetic mean amount of beer consumed by a customer in Kilroys is 6.5 liters with a standard deviation of 2 liters. According to Chebyshev\'s Theorem, what proportion (percent) of The customers drank between 3.30 liters and 9.70 liters of beer at The Kilroy\'s Pub? According to The Empirical Rule, what proportion of The customers consumed between 8.00 liters and 11.00 liters of beer? What you conclude about The symmetry of The distribution of beer consumption in liters at The Kilroy\'s Pub?

Solution

according to chebyshec theorem atleast 1-1/k^2 of data lie within k -standard deviation

9.7 = 6.5 + 1.6 * 2

and 3.3 = 6.5 - 1.6 * 2

=> interval (3.3,9,7) is 1.6 standard deviation from mean

=>
proportion of customers in this interval

= 1 - (1/1.6^2)

= 0.609375

b)

similarly

11 = 9.5 + 2 * 0.75

8 = 9.5 - 2 * 0.75

=> the interval (8,11) is 2 standard deviation from mean

according to empirical rule 95% of data lie within two standard deviation from mean

c)

the consumption of beer at kilroys pub is symmetric about mean