Question

The mean rate for cable television from a sample of households was $30 per month, with a standard deviation of $2.5 per month. Assume that the data set has bell-shaped distribution.

Between what two values do about 99.7% of the data fall?

Answer 1

Mean(u)= 30

Standard deviation (sigma)= 2.5

Let X~N(u,sigma²)

Z statistic = (x-u)/sigma

We have given that

Prob (x1<x<x2)=99.7%=0.997

=Prob (z1<z<z2)=0.997

Z1=(x1-u)/sigma.       ...........(i)

Z2= (x2-u)/sigma.       .......(ii)

From standard normal table we have →prob(-2.968<z<2.968)=0.997

Thus x1= sigma*(-2.968)+30=22.581

x2= sima*2.968+30=37.419

Ans→ the two value are →22.581, and 37.419

Thanks!

Stay safe!