# SOLUTION: Using the normal distribution, find the probability that a population with a mean of 35 and a standard deviation of 8 will produce a sample mean of less 34 in a sample of size 64.

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: Using the normal distribution, find the probability that a population with a mean of 35 and a standard deviation of 8 will produce a sample mean of less 34 in a sample of size 64.      Log On

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 Question 418355: Using the normal distribution, find the probability that a population with a mean of 35 and a standard deviation of 8 will produce a sample mean of less 34 in a sample of size 64.Answer by Edwin McCravy(8879)   (Show Source): You can put this solution on YOUR website!Using the normal distribution, find the probability that a population with a mean of 35 and a standard deviation of 8 will produce a sample mean of less 34 in a sample of size 64. ``` Find the test statistic Draw a normal curve. Draw a green line at -1. We want to find the area to the left of the green line. If you have the same kind of normal table as you find on this site http://www.stat.ucla.edu/~ywu/teaching/normal.pdf It gives the area from the far left to the z-score. So you will just go down the leftmost column to -1.0 and since there are no more decimals, go to the first column beside that and you see 0.1587. That's the desired probability, 0.1587 However, if you have the kind of normal table on this site http://www.mathsisfun.com/data/standard-normal-distribution-table.html This kind of table gives the area from the center line to the z-score. So you go down the leftmost column to 1.0 and since there are no more decimals, go to the first column beside that and you see 0.3413. However since that is the area between the center line and the z-score, you must subtract that value from 0.5 0.5000 -0.3413 ------- 0.1587 Edwin```