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So I have this problem that goes like this: Suppose the distribution of height over a large population of individuals is approximately normal. Ten percent of individuals in the population are over 72 inches tall, while the average height is 70 inches. What, approximately, is the probability that in a group of 100 people picked at random from this populatino there will be two or more individuals over 74 inches tall? I'm really quite stuck, can the sample of the population tell us the standard deviation?

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up vote 3 down vote accepted

It isn’t the sample that tells you $\sigma$, the standard deviation, it’s the rest of the information in the problem.

You’re told that the population mean is $70$ inches and that $10$% of the population is over $72$ inches tall, so $90$% of the population is at or below $72$ inches in height. Using a table of the standard normal distribution, find the $z$-score that has $90$% of the area to the left of it: it’s about $1.28$. That means that $72$ inches is about $1.28$ standard deviations above the mean of $70$ inches, so $2$ inches is about $1.28$ standard deviations. Now do a little arithmetic, and you’ll have $\sigma$.

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