Question

Use the Standard Normal Distribution table to find the indicated area under the standard normal curve.

Q1: Between z = 0 and z = 2.24
A1: 0 = 0.5000
2.24 = 0.9875
0.9875 – 0.5000 = 0.4875

Q2:To the left of z = 1.09
A2: 0.8621

Q3: Between z = -1.15 and z = -0.56
A3: -1.15 = 0.1251
-0.56 = 0.2877
0.1251 - 0.2877 = -0.1626

Q4: To the right of z = -1.93
A4: 1 – 0.0268 = 0.9732



Section 5.2: Normal Distributions: Find Probabilities

Q5: The diameters of a wooden dowel produced by a new machine are normally distributed with a mean of 0.55 inches and a standard deviation of 0.01 inches. What percent of the dowels will have a diameter greater than 0.57?

A5: z = x - µ / ó
= 0.57 – 0.55 / 0.01 = 2
=P (x > 0.57)
= P(z > 2)
= 1 – P (z < 2)
= 1 – 0.9772
= 0.0228

Q6: A loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 50. Find the probability that an applicant will have a rating greater than 260.

A6: z = x - µ / ó
= 260 – 240 / 50
= 0.4
=P (x > 260)
= P(z > 0.4)
= 1 – P (z < 0.4)
= 1 – 0.6554
= 0.9772

Answer 1

1. Right, but there should be a column in the table listing area from mean to Z score, so you could have eliminated some of the steps you indicate.

4, 5, 6. Likewise, there should be a column indicating the area in the larger portion and smaller portion to find these answers more directly.

6. You have a subtraction error. 1 - 0.6554 ≠ 0.9772.

Otherwise, you are correct.