Answer to Question #297905 in Statistics and Probability for Rovel May

Question

Make a study about how many sheets of paper you consumed weekly in answering your self learning modules record the quantity total number of sheets per subject then construct a probability distribution compute the mean variance and the standard deviation of the probability distribution you made and third pret the result then find out how many weeks you will consume 50 sheets of pad paper

Answer 1

let X denote the number of subjects

we may represent the probability distribution from our study as below

x 1 2 3 4 5

p(x) 3/20 7/25 7/50 13/50 17/100

we obtain the mean as below

( ( 1* 3/20 ) + ( 2 * 7/25 ) + ( 3* 7/50 ) + ( 4 * 13/50 ) + ( 5 * 17/100 ) ) = 3.02 which is the required mean.

we obtain the variance as below

= ( ( 1² * 3/20 ) + ( 2² * 7/25 ) + ( 3² * 7/50 ) + ( 4² + 13/50 ) + (5² * 17/100 ) ) - ( 3.02² )

= ( 10.94 - 9.1204 ) = 1.8196 which is the required variance

we obtain the standard deviation as below

= (variance)^1/2 = ( 1.8196 )^1/2 = 1.348925498 which is the required standard deviation.

Thus the number of weeks required to use 50 sheets of paper is obtained as below

= ( 50/3.02 ) = 16.55629139 which is approximately 17 weeks.