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now in Part A youre supposed to figure out how many students there are so every confidence interval is a point estimate plus or minus a margin of error so in this case were estimating the proportion so our point estimate is P hat and our margin of error is made up of a critical value Z star and a standard error which in this case is the square root of P hat times 1 minus P hat over N so we need to figure out what P hat is now P hat is going to be the very middle of this interval so we can find the middle of the interval by adding the two values and dividing by 2 so P hat is 0.7 so the middle of this interval is 0.7 so if you take point 7 and you add and subtract a margin of error you end up with this interval so lets figure out how much the margin of error is so from point seven two point eight one six is point one one six so now we know the margin of error is point one one six so this quantity here has to equal point one one six so lets fill in what we have we know P hat is 0.7 s
