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Hello everyone.
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In this lesson, we're exploring a fascinating application of statistical principles to educational planning.
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We're tasked with determining how many students must be admitted to their first year of studies to ensure that with a probability of at least 90%, at least 50 students graduate on time, given that on average 30 % of students complete their studies on time.
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This scenario is a great example of how statistical analysis can aid in decision -making processes.
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Let's break down the problem using the principles of expected value.
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You standard deviation and the normal approximation to the binomial distribution.
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Understanding the problem.
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So let's take a look at what's given.
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So on average, 30 % of students complete their studies on time.
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And the desired number of students students graduating on time is 50, which is going to be our k.
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Our 30 % was going to be our p.
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And then our desired probability, p, is greater than or equal to 90%.
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And this would mean our where z -score corresponding to p equals 1 .28155 from the standard normal distribution for 90 % confidence.
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Statistical approach.
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Expected value.
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The expected number of students graduating on time can be calculated using e equals n times p, where n is the total number of students admitted and p equals 0 .3 is the probability of graduating on time.
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Standard deviation...