Question

Average talk time between charges of a recently introduced smartphone was determined to be 4 hours with a standard deviation of 0.8 hours. The shape of the data distribution is not known.

Required of you: a) Compute the estimated proportion of smartphones that would have a talk time between 2.4 and 5.6 hours.

b) What would your answer be if we were interested in the proportion of smartphones having a talk time of more than 6 hours?

Answer 1

Ans:

We use Chebyshev's rule,when shape of the data distribution is not known.

a)

2.4 and 5.6 are 2 standard deviations below and above the mean respectively.

k=2

So,the estimated proportion of smartphones that would have a talk time between 2.4 and 5.6 hours

=1-(1/2^2)=1-0.25=0.75

b)6 is 2.5 standard deviation above the mean.

The estimated proportion of smartphones that would have a talk time between 2 and 6 hours

=1-(1/2.5^2)

=0.84

So, 0.16 falls beyond 2 and 6 hrs,hence half of it i.e. 0.08 will fall above 6 hrs.

0.08