Question

The mean number of minutes for app engagement by a tablet user is 8.2 minutes. Suppose the standard deviation is one minute. Take sample of size 70. Find the probability that the sum of the sample is at most 10 hours.

Answer 1

let Xi is number of minutes for app engagement so

E(Xi)=8.2                      SD(Xi) =1       this gives Var(Xi)=1

now n=70

let Y is total of time of minutes for app engagement for all 70 samples then

Y=X1+X2+.....+X70

so

E(Y)=E(X1+X2+....+X70) =E(X1)+E(X2)+....+E(X70) =8.2+8.2+...+8.2 =8.2*70 =574

Var(Y)=Var(X1+X2+....+X70) =Var(X1)+Var(X2)+....+Var(X70)=1+1+....+1=1*70 =70

10 Hours means 10*60=600 minutes

we have to find P(Y<600)

now