The heights of 1000 students are normally distributed with a mean of 177.5 centimeters and a...

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?

(d) greater than or equal to 191.0 centimeters?

Solutions

Expert Solution

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:

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!

orchestra answered 1 year ago

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