The following frequency distribution shows the monthly stock returns for Home Depot for the years 2003 through 2007. Over the time period,the following summary statistics are provided: Mean = 0.31%,Standard deviation = 6.49%,Skewness = 0.15,and Kurtosis = 0.38.The probability that the return is less than −5% if the return is normally distributed is _______.
A) 0.2061
B) 0.2740
C) 0.2841
D) 0.2358

Question

The following frequency distribution shows the monthly stock returns for Home Depot for the years 2003 through 2007.  Over the time period,the following summary statistics are provided: Mean = 0.31%,Standard deviation = 6.49%,Skewness = 0.15,and Kurtosis = 0.38.The probability that the return is less than −5% if the return is normally distributed is _______.
A) 0.2061 
B) 0.2740 
C) 0.2841 
D) 0.2358

Quizplus · Accepted Answer

To find the probability that the return is less than -5%, we need to standardize -5% using the mean and standard deviation provided, assuming that the returns are normally distributed.

Standardized value = (x - mean) / standard deviation

Standardized value = (-5% - 0.31%) / 6.49% = -0.797

Looking up the area to the left of -0.797 in a standard normal distribution table, we get 0.2061. Therefore, the probability that the stock return is less than -5% is 0.2061 or approximately 20.61%.

Hence, the correct answer is option A.

The Following Frequency Distribution Shows the Monthly Stock Returns for Home