Shoppers at a mall have a mean weight of 70 kg with a standard deviation of 10 kg. An elevator at the mall holds a maximum of 6 people, and safety engineers are curious about the average weight of shoppers on a full elevator. Suppose that we take random samples of 6 shoppers and calculate the mean weight x ˉ on top of the shoppers in each sample.
Solution:
Let variable x represent the weight of a shopper at the mall.
Assuming this variable has a normal distribution with mean μ= 70kg and standard deviation σ = 10kg.
There are random samples of 6 shoppers. That is sample size (n) = 6
The mean of the sample (μₓ) is the same as the mean of the population (μ), hence:
μₓ = μ = 70 kg
The standard deviation of the sample (σₓ) is equal to the standard deviation of the population (σ) divided by the square root of the sample size (n).. Hence:
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