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Hello students, let us do this.
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Test scores are normally distributed with population mean mu equal to 70 and standard deviation sigma equal to 10.
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B .t.
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We are asked to find probability that a randomly selected student will have score between 50 and 90.
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Probability of 50 less than x less than 90.
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This will be probability of x less than 90 minus probability of x less than 50.
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The formula of z score is z equal to x minus mu upon sigma.
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With this for x equal to 90, we get z score as 2 and corresponding below probability 0 .9772.
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For x equal to 50, the z score we get as minus 2, corresponding below probability 0 .0228.
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So, subtracting the probability of z equal to minus 2 from probability of z equal to 2, we get difference of these two probabilities as 0 .9544.
01:08
This is the probability that x will lie between 50 and 90.
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Showing this on the standard normal curve or the normal curve having mean equal to 70, the mean will lie at the center of the normal curve.
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This is mean.
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The ask probability is probability for x equal to 50 and for x equal to 90.
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All this area is the probability.
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This probability is 0 .9544...