A business woman wants to open a coffee stand across the street from a competing coffee company. She notices that the competing company has

Question

A business woman wants to open a coffee stand across the street from a competing coffee company. She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers. Suppose she takes a random sample of 31 days. Identify the following to help her decide whether to open her coffee stand, rounding to the nearest whole number when necessary:
μ =_____customers per day
σ =_____customers per day
n =____
μ-x =____
σ-x =_____customers per day

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Minh Khuê 5 years 2021-07-24T11:28:34+00:00 1 Answers 62 views 0

Answers ( )

  1. thucuc
    0
    2021-07-24T11:30:28+00:00
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    Answer:

    μ = 170 customers per day

    σ = 45 customers per day

    n = 31

    \mu_x = 170

    \sigma_x = 8

    Step-by-step explanation:

    Central Limit Theorem

    The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

    For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

    She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers.

    This means that \mu = 170, \sigma = 45

    Suppose she takes a random sample of 31 days.

    This means that n = 31

    For the sample:

    By the Central Limit Theorem, the mean is \mu_x = 170 and the standard deviation is \sigma_x = \frac{45}{\sqrt{31}} = 8

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