For the total population of a large southern city, mean family income is $34,000, with a standard deviation (for the population) of $5,000. Imagine
that you are taking subsample of 200 city residents. What is the Z score for
$33,000?

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) what is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive? (b) what is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) what proportion of bags contains more than 1225 chocolate chips? (d) what is the percentile rank of a bag that contains 1425 chocolate chips?

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

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