Final answer:
To calculate probabilities using the standard normal distribution and the z-table, you can find the areas to the left or right of specific z-scores. For P(Z<1.40), the area to the left of 1.40 is 0.9192. For P(Z>1.40), the area to the right of 1.40 is 0.0808. And for P(-3 ≤ Z < -0.03), the area between -3 and -0.03 is -0.4833.
Step-by-step explanation:
To calculate the probabilities, let's use the standard normal distribution and the z-table. A z-score represents the number of standard deviations an observation or value is from the mean.
a. To find P(Z<1.40), look up the z-score 1.40 in the z-table. The area to the left of 1.40 is 0.9192.
b. To find P(Z>1.40), subtract the area to the left from 1. The area to the right of 1.40 is 1 - 0.9192 = 0.0808.
c. To find P(-3 ≤ Z < -0.03), subtract the area to the left of -0.03 from the area to the left of -3. The area to the left of -0.03 is 0.4846 and the area to the left of -3 is 0.0013. Subtracting these, we get 0.0013 - 0.4846 = -0.4833.