the heights of 1000 students in a college are normally distributed with a mean 5’10” and SD 2”.

Question

the heights of 1000 students in a college are normally distributed with a mean 5’10” and SD 2”. Use 68% for the region from the mean to 1-SD on either side; 94% for the region from the mean to 2-SD on either side and 98% for the region from the mean to 3-SD on either side. Find the approximate number of students in each range of the heights:28) 5’8”–6’29) 5’6”–6’2”30) Above 5’10”31) Below 6’32) Above 5’8”33) 5’8”–6’4”

Answer 1

Since this question has many sub-questions, it is easier to answer all of them if you understand the whole situation first. In other words, figure out how many students are in each region determined by the standard deviation. For example, 34% of the students are in the region from the mean to the mean plus one standard deviation. That means 340 students are between 5'10" and 6' (since mean+standard deviation = 5'10" + 2" = 6'). Notice that we used 34% instead of 68%, because of the 68% within one standard deviation of the mean, half of them are greater than the mean and half of them are less than the mean. Performing this calculation for all of the regions considered yields the following table, where each row represents one standard deviation:

Under 5'4" : 10 students

5'4"-5'6" : 20 students

5'6"-5'8" : 130 students

5'8"-5'10" : 340 students

5'10"-6' : 340 students

6'-6'2" : 130 students

6'2"-6'4" : 20 students

Above 6'4" : 10 students

 

Using this table, it is easy to calculate the total number of students in each of the requested ranges.

 

28) 5'8"-6' : 680 students

29) 5'6"-6'2" : 940 students

30) Above 5'10" : 500 students

31) Below 6' : 840 students

32) Above 5'8" : 840 students

33) 5'8"-6'4" : 830 students