Core Question ???

[k31453]

any idea how to do this question ??

The heights of 300 students are approximately normally distributed with a mean of 168 cm and a standard deviation of 4 cm.  The number of students with a height between 164 cm and 176 cm is closest to?

[fred42]

68% of values lie within one SD of the mean so 68% are of height between 164 cm and 172 cm which is 34% to the right and 34% to the left.

Now 95% of values lie within 2 SD of the mean or between 160 cm and 176 cm. That means 47.5% lie between 168 cm and 176 cm. So (47.5 + 34)% of people must have a height between 164 cm and  176 cm giving 81.5% of 300 = 244.5 or 245 people.

[Stick]

Definitely put the standard deviation bell curve into your bound reference. I find the 68, 95, 99.7 % rule really cumbersome, so instead I just read off a curve that has all the percentages ready.

[FlorianK]

A bit more in detail:

Split it up into 164to172 + 172to176

164 and 172 is 1 standart deviation each away from the mean, therefore 68% of the students are in that range.

You can split up 172 to 176 into [(0 to 176)-(0-172)]
97.5% of the students are between 0 and 176 (95% rule for 2 standart deviations)
97.5%=95+(100-95)/2

84.0% of the students are between 0 and 172 (68% rule for 1 standart deviation)
84.0%=68+(100-68)/2

Students between 172 to 176 = 97.5-84= 13.5%

Students between 164 and 176 =68%+13.5%=81.5%

300*81.5/100=244.5~245students