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Sampling Distribution of a Median

APSTAT-VJXOIL

All of the numbers from 1 to 50 are written on slips of paper and placed in a hat. The slips are thoroughly mixed, five slips of paper are chosen, and the median is recorded. This process is repeated a total of 150 times and the medians are displayed in a dotplot:

Based on this sampling distribution, which of the following statements is true?

A

There is a $2\%$ chance of obtaining a sample median of $45$ or more.

B

There is no chance of obtaining a sample median of $45$ or more because the population median is $25.5$.

C

There is an $8.7\%$ chance of obtaining a sample median less than $15$.

D

There is a $12.7\%$ chance of obtaining a sample median less than $15$.

E

There is an $87.3\%$ chance of obtaining a sample median less than $15$.