I am doing something wrong here. I believe that I am notcoming up with the corre

Question

I am doing something wrong here. I believe that I am notcoming up with the correct z-score for my equation. Please provide me with some instruction here. Q: The random variable x is normally distributed witha mean of 75 and a standard deviation of 15.0. For thisdistribution, the twenty-third percentile(P23) is: This is what I have come up with thus far: x-75=15(-0.1064) >>x=75-15.96=59.04 Yet the answers I have to choose from are:65.7, 63.9, 86.1 & 84.3 I will rate Lifesaver. Please explain tome how to come up with the correct z value, so I can lookit up in Table 3 (Areas of the Stand. Norm. Dev.) Thank you!!! I will rate Lifesaver. Please explain tome how to come up with the correct z value, so I can lookit up in Table 3 (Areas of the Stand. Norm. Dev.) Thank you!!!

Explanation / Answer

For these types of problems, it is a 3 step process. 1) Turn the percentile into a z-score. This is done bylooking up the p-value in a z-table and grabbing the correspondingz-score. In this case, the 23% implies z = -.74. 2) Write down the equation for z-score and plug in the knownvalues. In this case, we have z = -.74 = (x - ) / = (x - 75) / 15 3) Solve for X. -.74 * 15 = x - 75 x = 75 + -.74 * 15 = 63.9

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