Question

The heights of 1000 students are normally distributed with a mean of 177.5 centimeters and a standard deviation of 6.7 centimeters. Assuming that the heights are recorded to the nearest​ half-centimeter, how many of these students would be expected to have heights

​(a) less than 167.0 centimeters?

​(b) between 173.5 and 185.0 centimeters​ inclusive?

​(c) equal to 180.0 ​centimeters?

​(d) greater than or equal to 191.0 ​centimeters?

Answer 1

Using excel to solve the problem I get:

Mean	177.5
Standard Deviation	6.7
Total Number of students	1000
	Condition	Probability	Expected Number of students	Rounded Expected Number of students
​(a) less than 167.0 centimeters?	<167	0.04109919	41.09918907	41
​(b) between 173.5 and 185.0 centimeters​ inclusive?	173.5<=x<=185	0.59326716	593.2671631	593
​(c) equal to 180.0 ​centimeters?	=180	0.05553951	55.53950703	56
​(d) greater than or equal to 191.0 ​centimeters?	>=191	0.02977672	29.77672353	30

The calculations are:

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