How do I work this problem to get the answer for 0.019? Is there any work involv

Question

How do I work this problem to get the answer for 0.019? Is there any work involved or do I simply refer to the table to find the proportion in the tail?  

A random sample is obtained from a population with a mean of ? = 40 and a standard deviation of ? = 9. Which of the following probability values is closest to a a sample mean of M = 45, with sample of n = 14 scores?

a.

.00003

b.

.006

c.

.019

<img data-cke-saved-src="https://bb2.uhd.edu/courses/1/20183030582/content/_511319_1/sclb_extras/images/check.png" src="https://bb2.uhd.edu/courses/1/20183030582/content/_511319_1/sclb_extras/images/check.png" alt="correct" "="">  

586 APPENDIX B STATISTICAL TABLES Proport ion ion in Tail Between Mean and z in Body Between Mean and z in Body 9332 9345 9357 9370 9382 4772 4778 4783 4788 4793 4798 4803 4808 4332 4345 4357 4370 4382 9772 9778 9783 9788 9793 9798 9803 9808 9812 0228 0222 0217 0668 1.52 0643 0207 0202 0197 0618 0606 0594 0582 0571 0559 0548 0537 0526 0516 0505 0495 0485 9406 9418 4406 4418 4429 0183 9441 9452 9463 9474 9484 9495 9505 4821 4826 4830 4834 4838 4842 4846 4850 9821 9826 9830 9834 9838 9842 9846 9850 9854 9857 9861 9864 9868 9871 9875 9878 4452 4463 4474 4484 4495 0179 0170 0166 0162 0158 0154 4505 9525 9535 9545 9554 9564 9573 9582 9591 9599 0465 0455 0446 0436 0427 0418 0409 0401 4525 4535 4545 4554 4564 4573 4582 4591 4599 0146 .0143 0139 0136 0132 0129 0125 0122 4857 4861 4864 4868 2.20 -4875 4878

Explanation / Answer

Given that,

sample size (n) = 14

Population mean (mu) = 40

Population standard deviation (sigma) = 9

Sample mean (Xbar) = 45

The z-score for Xbar = 45 is,

Z = (Xbar - mu) / (sigma / sqrt(n))

= (45 - 40) / (9 / sqrt(14))

= 2.079

Now we have to see probability for z = 2.079

By using given table for z = 2.079 probabiility = 0.0192

So option c) is correct.

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