Determine the area under the standard normal curve that lies to the left of

a. $2.24$

b. $-1.56$

c. $0$

d.$-4$

We need to determine the area under the standard normal curve that lies to the left for the given values.

Since $2.24$is positive, we use the standard normal table of positive $z$scores. First , we go down to the left handed column labeled $z$to $2.24$.Then going across that row to the column labeled $0.04$, we reach $0.9875$.

Therefore, the area under the standard normal curve that lies to the left of$2.24$is,$0.9875$.

Since $-1.56$is negative, we use the standard normal table of negative $z$scores. First we go down to the right hand column labeled $z$to $-1.5$. Then going across that row to the column labeled $0.06$, we reach $0.0594$. Therefore, the area under the standard normal curve that lies to the left of$-1.56$is,$0.0594$.

We use the standard normal table. First, we go down to the left-hand column, labeled $z$to $0.0$. Then, going across that row to the column labeled $0.00$, we reach $0.5000$.

Therefore, the area under the standard normal curve that lies to the left of$0.00$is,$0.5000$.

Since $-4$is negative, we use the standard normal table for negative $z$scores. But we have no $-4.00$in the table. So, the area under the standard normal curve that lies to the left of$-4.00$is,$0.0000$.