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In this problem, it is said that the commute time to work in the u .s.
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Has a bell -shaped distribution with a population mean of 24 .4 minutes and a population standard deviation of 6 .5 minutes.
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We need to determine what commute time corresponds to a z score of 1 .5 and what commute time corresponds to a z score of negative 1 .5.
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Now, recall the formula for the z score.
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This is given by x minus mu divided by sigma, where x is the raw score.
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Mu is the mean, and sigma is the standard deviation.
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Now, we want to find the commute times which correspond to particular z score, so we need to find the values of x.
00:42
Let us solve this equation for x.
00:44
We will get that x minus mu is equal to z times sigma, and from here we can obtain that x is equal to z sigma plus mu.
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Now, let us solve the given problems.
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So first of all, we need to determine the commute time, which corresponds to a z score of 1 .5...