Question

Assume that the variable under consideration has a density curve. The area under the density curve that lies between 13 and 17 is 0.412. What percentage of all possible observations of the variable are either less than 13 or greater than 17​?  

Answer 1

As it is given that area under curve between 13 and 17 is 0.412

and we know that area under curve of a pdf is always equal to 1

and here we need to find the probability such that values lies less than 13 and more than 17

i.e.,

let X be the random variable given above.

Then

P(X < 13) + P(13 < X < 17) + P(X > 17) = 1 {By the fundametal property of pdf}

P(X < 13 ) + 0.412 + P(X > 17) = 1

P(X < 13 ) + P(X > 17) = 1 - 0.412 = 0.588

So 58.8 % of possible values are less than 13 and greater than 17