Suppose a normally distributed set of stock prices with 3500 observations has a mean of 101 and a standard deviation of 10. Use the 68-95-99.7 Rule to determine the number of observations in the data set expected to be between the values 91 and 121.

The number of observations in the data set expected to be between the values 91 and 121 is of 2853.

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 = 101, Standard deviation = 10

Percentage of of observations in the data set expected to be between the values 91 and 121.

91 = 101 - 10

So 91 is one standard deviation below the mean.

121 = 101 + 2*10

So 121 is two standard deviations above the mean

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

Of those 50% below the mean, 68% are between one standard deviation below the mean(91) and the mean(101).

Of those 50% above the mean, 95% are between the mean(101) and two standard deviations above the mean(121).

So the percentage of observations in this interval is of:

Number of observations in the interval

81.5% of 3500. So

0.815*3500 = 2853

The number of observations in the data set expected to be between the values 91 and 121 is of 2853.

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