Use Table to obtain the areas under the standard normal curve. Sketch a standard normal curve and shade the area of interest in each problem.

Find the area under the standard normal curve that lies

a. either to the left of $-1$or to the right of $2$.

b. either to the left of $-2.51$or to the right of $-1$.

To the left of $-1$is the following area:

Because the given integer $-1$is negative, the conventional normal table of negative $z$scores is applied. To begin, move down the right hand column labeled' $z$'to $-1.0$and then across the row to the column labeled'$0.00$'to get $0.1587$.

Right-hand side of $2$:

Right-hand area $=1$- Left-hand area

Because the given number 2 is positive, the typical normal table of positive $z$scores is applied. To begin, move down the left hand column labeled' $z$'to $2.0$and then across the row to the column labeled' $0.00$'to get $0.9772$

Consequently the area under the standard normal that lies to the right of localid="1650968971458" $2.0$is localid="1650968976364" $1-0.9772=0.0228$

The area is$0.1587+0.0228=0.1815$.

Because the given integer $-2.51$is negative, the typical normal table of negative $z$scores is utilised in the area to the left of $-2.51$. To begin, move down the right hand column labelled $z$'to $-2.5$and then across the row to the column labeled' $0.01$'to get $0.0060$.

Area to the right of $-1$:

Area to the right $=1$- Area to the left

Because the given integer $-1$is negative, the conventional normal table of negative $z$scores is applied. To begin, move down the right hand column labeled' $z$'to $-1.0$and then across the row to the column labeled' $0.00$'to get $0.1587$.

Thus, the area under the standard normal that lies to the right of localid="1650969349641" $-1$is localid="1650969354791" $1-0.1587=0.8413$

The area is$0.0060+0.8413=0.8473$.