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In this problem, the variable is normally distributed with mean, mu equals 64, and standard deviation sigma equals 2.
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Based on this information alone, we want to answer a through d below.
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This question is challenging your understanding of how to answer questions related to normally distributed random variables.
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To solve, we utilize the following relevant information.
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On the left, we have information on how to map up z score onto probability for area under normal distribution for a random variable or rather standard normal variable z.
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On the right we have inspiration how to map a non -standard normal onto a standard normal.
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Because our variable has non -mean 0 or mean non -zero or mean non -zero and standard deviation non -1, we have to use the conversion z equals x -9v6 u over sigma.
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So we can use this to answer a through d.
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A, what is the probability x is between 50 and 70? this is equivalent to the probability z is between the z scores 58 minus 64 over 2 equals negative 3 and 70 minus 64 over 2 equals 3.
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From a z table this is 0 .997 3.
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And b, what are the quartiles? we look for the z scores that separate our tails of our normal distribution in a .25 area.
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These are z equals plus or minus .67...