When doing polling, for instance to figure out how popular a given candidate is, a common trick is to just ask N many people whether they support that candidate, and take the support to be the faction of people who say yes: if 70 people support the candidate out of 100 asked, we estimate the support at 70% or 0.7. Suppose that the probability a person supports a candidate is p, which you do not know. Let pn be the fraction of N people polled who support the candidate: total supporters divided by N people polled. 1) What is the distribution of N * în? 2) Show hat the expected value of PN is p, i.e., PN is a valid estimator for p. If you want your estimated value of p to be accurate, you want your 'error' on PN to be small. 3) How many people N should you poll to guarantee the expected squared error on N is less than 4) How many people N should you poll to guarantee the expected squared error on py is less than e, even if you don't know p?

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 126.3-cm and a standard deviation of 2.5-cm. For shipment, 22 steel rods are bundled together. Find the probability that the average length of rods in a randomly selected bundle of steel rods is less than 124.8-cm. P(X < 124.8-cm) = %3D Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

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