Respuesta :
Answer:
She should order 2400 coupons.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
She would like 40% of customers in the population to receive the highest possible discount, with an SEP of 0.01 for this population.
This means that [tex]p = 0.4, s = 0.01[/tex]
How many coupons should she order?
We have to find n. So
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]0.01 = \sqrt{\frac{0.4*0.6}{n}}[/tex]
[tex]0.01\sqrt{n} = \sqrt{0.4*0.6}[/tex]
[tex]\sqrt{n} = \frac{\sqrt{0.4*0.6}}{0.01}[/tex]
[tex](\sqrt{n})^2 = (\frac{\sqrt{0.4*0.6}}{0.01})^2[/tex]
[tex]n = 2400[/tex]
She should order 2400 coupons.
