Question 59

Closing prices for a certain stock were recorded each day for a week as follows: Monday: 17.94; Tuesday: 18.19; Wednesday: 18.06; Thursday: 17.54 and Friday: 17.38. If the monthly average (arithmetic mean) was 18.43 and the standard deviation was 0.27, how many days during this week did the closing price fall within two standard deviations from the average?

Solution

Closing prices for stocks on each day of the week are given
Monday - 17.94
Tuesday - 18.19
Wednesday - 18.06
Thursday - 17.54
Friday - 17.38
Given average is 18.43 and the standard deviation is 0.27.
Two standard deviations = (2)(0.27) = 0.54
Two standard deviations below the mean = 18.43 - 0.54 = 17.89
Two standard deviations above the mean = 18.43 + 0.54 = 18.97
Values should lie between 17.89 and 18.97.
Days during this week, the closing price falls within two standard deviations from the average: Monday, Tuesday, and Wednesday values are in the given range.
Therefore, the answer is 3.


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