explain how to use the standard normal table to find the probability associated with the shaded area under…

Answer:

To find the probability associated with the shaded area between (z = 0.4) and (z=1.9) using the standard - normal table:

1. Look up the cumulative probability for (z = 1.9) in the standard - normal table. The table gives the area to the left of (z). Let (P(Z<1.9)) be the value obtained from the table.
2. Look up the cumulative probability for (z = 0.4) in the standard - normal table. Let (P(Z < 0.4)) be the value obtained from the table.
3. The probability of the shaded area (P(0.4<Z<1.9)=P(Z < 1.9)-P(Z < 0.4)). Subtract the cumulative probability of (z = 0.4) from the cumulative probability of (z = 1.9) to get the probability of the area between (z = 0.4) and (z = 1.9).

Explanation:

Step1: Find (P(Z < 1.9))

Use the standard - normal table.

Step2: Find (P(Z < 0.4))

Use the standard - normal table.

Step3: Calculate (P(0.4<Z<1.9))

(P(0.4 < Z<1.9)=P(Z < 1.9)-P(Z < 0.4))