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, half of the music students practice between 5.3 to 10.7 hours each week. What percentage of the students study less than 5.3 hours each week?

Answer 1

Answer with explanation:

Mean of the Normal Distribution = 8

Standard Deviation = 4

50% of the students practice between 5.3 hours to 10.7 hours.

→Drawing the normal Distribution Curve,and Observing

→→→50 % of population lie on both side of mean.

Total Population = 16→∵ mean=8

When curve is symmetrical, Mean = Mode =Median

→→→Population which lie on left of 5.3 can be calculated as

Between 1 standard deviation from both side of mean lie 68% of Data.

So, Between 4 to 8, lie 34% of Data.

Between 4-5.3, % of data lie , $\frac{34\times 1.3}{4}=11.05%$ of Data.

Between 0-4 lie , $\frac{32}{2}=16%$ of Data.

So,% of Data value ,that is population that lie on left of 5.3 hours =16+11.05=27.05%

So, Percentage of Population which lie on left of 5.3,that is study less than 5.3 hours each week = 33.125%