Question

A tour guide company is trying to decide if it is going to increase the cost of its tours to cover its sunk costs. They find that the average sunk cost per tour is $58, with a standard deviation of $18. If they take a random sample of 36 tours, identify each of the following to help them make their decision and round to the nearest hundredth if necessary:
mean

std

sample mean

n=

Answer 1

Answer:

$\bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}}$

And then we have that:

$n = 36 , \bar X = 58, s = 18$

So then the parameters for the sample mean would be:

$\mu_{\bar X}= 58$

$\sigma_{\bar x}= \frac{18}{\sqrt{36}}= 3$

Step-by-step explanation:

For this case we have the following info given :

$\bar X = 58$ represent the sample mean obtained

$s= 18$ represent the sample deviation calculated from the followojg formula:

$s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2)}{n-1}}$

We also know that the sampel selected for this case is n =36.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

For this case our sampel size is n = 36>30 so then we can apply the central limit theorem.

And for this case we know that the sample mean have the following distribution:

$\bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}}$

And then we have that:

$n = 36 , \bar X = 58, s = 18$

So then the parameters for the sample mean would be:

$\mu_{\bar X}= 58$

$\sigma_{\bar x}= \frac{18}{\sqrt{36}}= 3$