Question

Suppose that wait times for customers at a fast food restaurant have a mean of 2.7 minutes with a standard deviation of 0.2 minutes. Using Chebyshev's Theorem, what is the minimum percentage of customers who wait between 2.1 minutes and 3.3 minutes? Round your answer one decimal place.

Answer 1

Solution:

Given, the distribution have

mean = 2.7 and SD = 0.2

According to Chebyshevs Theorem ,  

P[( - k) < X < ( - k) ] =  

Now ,

2.1 = 2.7 - (3 * 0.2) = - 3

3.3 = 2.7 + (3 * 0.2) =   + 3

So , k = 3

So ,

Minimum percentage between 2.1 and 3.3 is

=

= 1 - [1/3²]

= 1 - [1/9]

= 8/9

= 0.889

= 88.9 %

Answer : 88.9 %