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Answer:
The number of observations in the data set expected to be below a value of 231 is of 4793.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 195
Standard deviation = 12
The normal distribution is symmetric, which means that 50% of the observations are above the mean and 50% are below.
Proportion of observations below 231:
231 = 195 + 3*12
So 231 is three standard deviations above the mean.
Of the 50% of observations below the mean, all are below 231.
Of the 50% of observations above the mean, 99.7% are between the mean of 195 and three standard deviations above the mean(231).
So, the proportion of observations below 231 is:
Out of 4800:
0.9985*4800 = 4793
The number of observations in the data set expected to be below a value of 231 is of 4793.