Question

What is the new deviation score (distance from the sample mean or estimated population mean) for the specification upper limit and lower limit, respectively? Then divide the deviation scores in Q2 by the estimated population standard deviation to standardize these scores (gives a Z score).

54	58	57	56
56	55	54	55
57	56	57	55
56	56	55	56
57	54	57	55

Answer 1

Xi	fi	xi*fi	(Xi-mean)^2	(Xi-mean)^2 * fi
54	3	162	3.24	9.72
55	5	275	1	5
56	6	336	4	24
57	5	285	3249	16245
58	1	58	3364	3364
	20	1116		19647.72
Mean	55.8		sd	31.3430375
Low Lim	54
Upper Lim	58

Deviation score from mean for lower limit = 55.8 - 54 = 1.8

Deviation score from mean for upper limit = 55.8 - 58 = -2.2

Z Score for lower limit = 1.8 / 31.343 = 0.057

Z Score for upper limit = -2.2 / 31.343 = -0.07