Question

	Range Minimum:	0
	Range Maximum:	252
	Median:	12
	Mode:	3
	μ	21.1272
	n	566
	σ2	759.903
	σ	27.5663
	stdev	27.5663

	Clemente	Langford
raw score	21	29
Z score	-19.7705	-19.4803

What percentage of Chicago schools have a rate of misconduct that falls between Roberto Clemente Community Academy High School and Anna R. Langford Community Academy?

Answer 1

Let X be the random variable denoting the rate if misconduct in Chicago school.

Thus, X ~ N(21.1272, 27.5663) i.e. (X - 21.1272)/27.5663 ~ N(0,1).

The probability that the percentage falls between 21 and 29 is = P(21 < X < 29) = P[(21 - 21.1272)/27.5663 < (X - 21.1272)/27.5663 < (29 - 21.1272)/27.5663] = P[-0.0046 < (X - 21.1272)/27.5663 < 0.2856] = (0.2856) - (-0.0046) = 0.6124 - 0.4982 = 0.1142. (Ans).

[(.) is the cdf of N(0,1)].