If the linear correlation between typical daily temperature and coat sales is -0.737 and today the temperature is 2 standard deviations above the mean,what would you predict coat sales to be with respect to its mean?

A) 2.000 standard deviations below the mean sales
B) 1.474 standard deviations above the mean sales
C) 2.000 standard deviations above the mean sales
D) 1.474 standard deviations below the mean sales
E) 0.737 standard deviations below the mean height

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Pallavi Nagre · Accepted Answer

Final Answer : D, Explanation :  Since the correlation coefficient is negative, we expect a decrease in coat sales as temperature increases. Being 2 standard deviations above the mean indicates that we are in the upper 2.5% of temperature values, and if we use the inverse standard normal cumulative distribution function, we find that this corresponds to a z-score of approximately 2. Thus, we can expect coat sales to be 0.737(2) = 1.474 standard deviations below the mean sales. Since we already know that temperature is higher than usual, this decrease in sales corresponds to the predicted sales being below the mean. Therefore, we choose option D.

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