A logistics manager tracks the delivery time for shipments to a key customer. On average, the deliveries take 38 minutes with a standard deviation of 11 minutes. The delivery times are normally distributed. What is the expected value of the average delivery time for a random sample of 49 shipments?单项选择题
A
38 minutes
B
22.04 minutes
C
1.86 minutes
D
3.15 minutes

Question

A logistics manager tracks the delivery time for shipments to a key customer. On average, the deliveries take 38 minutes with a standard deviation of 11 minutes. The delivery times are normally distributed. What is the expected value of the average delivery time for a random sample of 49 shipments?单项选择题

A

38 minutes

B

22.04 minutes

C

1.86 minutes

D

3.15 minutes

BlackTom AI · Accepted Answer

We start by identifying the given information: the population mean delivery time is 38 minutes and the standard deviation is 11 minutes, with shipments distributed normally.
Option 1: 38 minutes. This is the expected value of the sample mean when sampling 49 shipments, because the mean of the sampling distribution of the sample mean equals the population mean (mu). The sample size affects the spread (standard error) but not the center.
Option 2: 22.04 minutes. This value resembles a calculation involving the standard error, perhaps 11 / sqrt(49) = 11 / 7 ≈ 1.571, but 22.04 does not correspond to any correct interpretation of the sampling distribution’s mean or standard error. It incorrectly combines or squares terms, leading to an implausible mean.
Option 3: 1.86 minutes. This is far smaller than any reasonable sampling distribution standard error for this problem; it could arise if one mistakenly took the standard error and squared or misapplied unit conversions, but it has no basis as the mean of the sample means.
Option 4: 3.15 minutes. Similar to option 3, this value might appear as a questionable standard error or a miscalculation, but it does not represent the expected sample mean and misunderstands how the sampling distribution centers around the population mean.
In summary, the correct interpretation is that the average of 49 deliveries has the same expected value as the population mean, 38 minutes, while the other options misstate or miscalculate the central tendency or mix up standard error concepts with the mean.

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