SOLUTION: Could someone please assist me with the following question. I am having problems with distribution of z scores. The distribution process is very confusing for me. I greatly appr

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Question 189874: Could someone please assist me with the following question. I am having problems with distribution of z scores. The distribution process is very confusing for me. I greatly appreciate someone helping me with this problem and showing the steps for completion. The problem is:
The test scores for 2000 students were normally distributed with a mean of 65 and a standard deviation of 5. Find the following:
a. The z-score corresponding to the test score of 70.
b. The probability that a tested student will have a score between 65 and 70.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The problem is:
The test scores for 2000 students were normally distributed with a mean of 65 and a standard deviation of 5.
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Help yourself by illustrating each problem you have.
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Draw a normal curve on an x-axis. Mark the mean = 65 in the middle
Note that s = 5
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Find the following:
a. The z-score corresponding to the test score of 70.
Use the formula z(x) = (x-u)/s
z(70) = (70-65)/5 = 5/5 = 1
Note: That means the score of 70 is one standard deviation to the right
of the mean.
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b. The probability that a tested student will have a score between 65 and 70.
Draw a normal curve over a z-axis.
The z-score of 70 is 1 (above).
The z-score of 65 is 0 because 65 is the mean.
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P(65 < x < 70) = P(0 < z < 1) = 0.34
You have to use a calculator or a z-chart to find that probability.
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Cheers,
Stan H.