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The number of music CDs sold weekly by a store follows a normal distribution with a mean of 455 and a standard deviation of 65. Which sentence summarizes this information?
• A. There is an 84% chance that the shop sells more than 390 CDs in a week.
• B. There is a 34% chance that the shop sells more than 390 CDs in a week.
• C. There is a 34% chance that the shop sells fewer than 390 CDs in a week.
• D. There is a 68% chance that the shop sells fewer than 390 CDs in a week.
• E. There is a 95% chance that the shop sells more than 390 CDs in a week.

Respuesta :

TopZ

Answer: To determine the probability of a certain range of CD sales in a week based on a normal distribution, you can use the empirical rule or the z-score.

The empirical rule states that for a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% falls within two standard deviations.

Approximately 99.7% falls within three standard deviations.

Given that the mean is 455 and the standard deviation is 65, we can find the z-score for selling 390 CDs:

Z = X−Mean​ / Standard Deviation

Z= 390−455 / 6 = -1

Now, referring to the empirical rule, within one standard deviation below the mean (Z = -1), we can say that approximately 34% of the data falls. Therefore, the correct sentence is:

C. There is a 34% chance that the shop sells fewer than 390 CDs in a week.

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