A manufacturer regularly receives shipments of computer chips. Over the past year the mean number of computer chips per shipment was 1200. If a shipment of 1456 chips was 1.6 standard deviations above the mean how many standard deviations below the mean was a shipment of 848 chips?

Rationale

A shipment of 848 chips was 2.2 standard deviations below the mean.

To find how many standard deviations below the mean a shipment of 848 chips is, we first determine the standard deviation using the information provided. Since a shipment of 1456 chips is 1.6 standard deviations above the mean of 1200, we can calculate the standard deviation and then apply it to find how far 848 chips is from the mean.

A (1.3) YOUR ANSWER

If a shipment were 1.3 standard deviations below the mean, the calculation would yield a value closer to the mean than 848 chips. This choice underestimates the distance from the mean, leading to an incorrect conclusion.

B (1.4) YOUR ANSWER

Similar to Option A, if a shipment were 1.4 standard deviations below the mean, the calculated value would still not reach as low as 848 chips. This choice does not account for the significant drop from the mean of 1200.

C (1.7) YOUR ANSWER

Choosing 1.7 standard deviations below the mean still does not sufficiently reflect how far 848 chips is from the average. This value remains too close to the mean, failing to encompass the actual distance involved in this scenario.

D (2) YOUR ANSWER

While this option is closer to the correct answer, it still falls short. Being 2 standard deviations below the mean would correspond to a value that is still higher than 848 chips, indicating an incorrect assessment of the shipment's distance from the mean.

E (2.2) CORRECT

This option accurately represents that a shipment of 848 chips is 2.2 standard deviations below the mean. By using the standard deviation calculated from the mean and the known shipment above the mean, we find that 848 chips indeed falls well below the average, confirming the correctness of this choice.

Conclusion

In summary, the shipment of 848 chips is correctly identified as being 2.2 standard deviations below the mean of 1200 chips. This calculation highlights the importance of understanding standard deviations in relation to the mean, as it allows us to effectively gauge how far a particular shipment deviates from average expectations.

A manufacturer regularly receives shipments of computer chips. Over the past year the mean number of computer chips per shipment was 1200. If a shipment of 1456 chips was 1.6 standard deviations above the mean how many standard deviations below the mean was a shipment of 848 chips?

A shipment of 848 chips was 2.2 standard deviations below the mean.

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