Question

Based on data from a​ college, scores on a certain test are normally distributed with a mean of 1527 and a standard deviation of 328.

Find the percentage of scores between 871 and 1691  ​% (Round to two decimal places as​ needed.)???????????

Standard Scores and Percentiles for a Normal Distribution ​(cumulative values from the​ left)
Standard score	​%	Standard score	​%
minus−3.0	0.13	0.1	53.98
minus−2.5	0.62	0.5	69.15
minus−2	2.28	0.9	81.59
minus−1.5	6.68	1	84.13
minus−1	15.87	1.5	93.32
minus−0.9	18.41	2	97.72
minus−0.5	30.85	2.5	99.38
minus−0.1	46.02	3	99.87
0	50.00	3.5	99.98

Answer 1

Answer

given that

mean = 1527

standard deviation = 328

871 is 2 standard deviation below the mean and 1691 is 0.5 standard deviation above the mean

using the given data table

there is 2.28% below 871 and 69.15% below 1691

this gives

= 69.15-2.28

= 66.87%

So, 66.87% of scores are between 871 and 1691