Question

You have a normal distribution of hours per week that music students practice. The mean of the values is 8 and the standard deviation of the values is 4. According to the normal distribution model that corresponds to this population, what percentage of the students practice between 6 to 10 hours per week? Use the graph of the standard normal distribution given below to find the percentage. 19% 30% 34% 38%

Answer 1

38%

Explanation:

Given that X,the hours per week the music student practice follow a normal distribution.

X:N(8,4)

We have to find the percentage of students who practice between 6 and 10 hours.

6<x<10 implies converting to z

We know z = (x-mean)/sigma = (x-8)/4

Hence 6<x<10 is equivalent to (6-8/4)<Z<(10-8/4)

= |z|<0.5

From std normal table we find this area equals = 0.1915+0.1915

=0.3830 = 0.38 (rounded off)

Hence required percentage = 0.38x100 = 38%