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I am taking a statistics course this semester, and this is part of our first homework assignment, only I don't know what the answer is even supposed to look like.

When the process is functioning correctly, the adhesive strength X is normally distributed with a mean of 200 N and a standard deviation of 10 N. Each hour, you make one measurement of the adhesive strength. You are supposed to inform your supervisor if your measurement indicates that the process has strayed from its target distribution.

a. Find P(X ≥ 203), under the assumption that the process is functioning correctly.

b. Based on your answer to part (a), if the process is functioning correctly, would a strength of 203 N be unusually large? Explain.

c. If you observed an adhesive strength of 203 N, would this be convincing evidence that the process was no longer functioning correctly? Explain.

Just to be clear, I don't necessarily need the answer, just what the answer would look like. I have no idea what Find P(X ≥ 203) means really. Thanks.

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    $\begingroup$ Here's a hint. X is random variable with known properties. You are asked what is the probability that X exceeds 203. Intuitively, X tends to hover around 200, so the probability that X is slightly greater than the mean of 200 should be a bit less than one half. $\endgroup$
    – dimitriy
    Commented Sep 17, 2014 at 4:33

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You are given a normally distributed attribute X with a known mean and standard deviation. As you may already know, the area under the normal curve is one (unity). By P(x ≥ 203), you are asked the area under the curve to the right of x=203. To determine that, calculate the number of standard deviation units x=203 lies above the mean (i.e., the z-score). Then from a z-table, you can read the area under the curve above the z-score you calculated which is the area to the right of x=203. That is p(x≥203).

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