Question

Using the standard normal table, find the following

probabilities:
(a) P(-1.15 ≤ z ≤ 1.56)
(b) P(0.15 ≤ z ≤ 2.13)
(c) P(z ≤ 1.00)
(d) P(z > 1.65)
Can Someone please explain the steps

Answer 1

To find probabilities using the standard normal table, locate the area to the left for each z-score and subtract, if needed, to find the probability within a range or to the right of a z-score.

Step-by-step explanation:

To find the probabilities using a standard normal table, you should follow these steps for each part of the question:

1. For P(-1.15 ≤ z ≤ 1.56), find the area to the left of z = 1.56 and then subtract the area to the left of z = -1.15.
2. For P(0.15 ≤ z ≤ 2.13), find the area to the left of z = 2.13 and subtract the area to the left of z = 0.15.
3. For P(z ≤ 1.00), simply find the area to the left of z = 1.00.
4. For P(z > 1.65), find the area to the left of z = 1.65 and subtract it from 1 to get the area to the right.

Remember, the standard normal distribution is symmetrical, and the total area under the curve is 1. When the table provides the area to the left of the z-score, you can use subtraction to find the area to the right if needed.