Descriptive Statistics

Question

z-score	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
%	53.98	57.93	61.79	65.54	69.15	72.57	75.80	78.81	81.59	84.13
​z-score	1.1	1.2	1.3	1.4	1.5	1.6	1.7	1.8	1.9	2.0
%	86.43	88.49	90.32	91.92	93.32	94.52	95.54	96.41	97.13	97.72
​z-score	2.1	2.2	2.3	2.4	2.5	2.6	2.7	2.8	2.9	3.0	3.5	4.0
%	98.21	98.61	98.93	99.18	99.38	99.53	99.65	99.74	99.81	99.87	99.98	99.997

The results of a certain medical test are normally distributed with a mean of

130 and a standard deviation of 12. A score above 142 is considered​ unhealthy). Use the given table to find the percentage of people with readings below 139.

Answer 1

Hi Kirshay! This question wants you to first figure out the z-score of your test statistic and then use the given table to figure out the percentile.

z = (x - mean) ⁄ standard deviation.

z = (139 - 130) ⁄ 12

z = 9 ⁄ 12

z = 0.75, rounded up to 0.8

This means that our value, 139, is 0.8 standard deviations away from the mean. Based on our table, we know that z = 0.8 results in 78.81%. Thus, 78.81% of the population has a reading below 139.