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Let denote the weights of grade 11 students.
Given that , we use this information to solve for the parameters and
To solve this, we shall apply the empirical rule. It states that, 99.7% of the data observed following a normal distribution lies within 3 standard deviations of the mean.
3 standard deviations below the mean can be written as, and is equal to the lower limit. For our case, the lower limit is 45. Thus,
3 standard deviations above the mean can be written as, and is equal to the upper limit. For our case, the upper limit is 60. Thus, .
To solve for the mean, we use equations and .
Adding equations and gives,
To solve for the standard deviation, we use equations and .
Subtracting equation from equation gives,
The normal curve of the normal distribution is given below.