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jasminbeganovic141
09.07.2021 •
Mathematics
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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Ответ:
μ = 170 customers per day
σ = 45 customers per day
n = 31
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean
and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
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](/tpl/images/1391/3467/4debd.png)
Suppose she takes a random sample of 31 days.
This means that![n = 31](/tpl/images/1391/3467/e739d.png)
For the sample:
By the Central Limit Theorem, the mean is
and the standard deviation is ![\sigma_x = \frac{45}{\sqrt{31}} = 8](/tpl/images/1391/3467/06720.png)
Ответ:
So first we take the total number of computers. Which will be 14 + 16 = 30 computers.
Since we have 16 pc computers, we will divide 16 by 30 and multiply it by 100 to get the percentage:
So: (16/30) x 100
There are 53.33% PC computers in the computer lab.