Answer:
The standard deviation for the sample mean distribution is [tex]\sigma_{\bar{X}}=\frac{136}{\sqrt{45}}=\frac{136\sqrt{5}}{15} \approx 20.274[/tex]
Step-by-step explanation:
The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population then the distribution of the sample means will be approximately normally distributed.
For the random samples we take from the population, we can compute the standard deviation of the sample means:
[tex]\sigma_{\bar{X}}=\frac{\sigma}{\sqrt{n}}[/tex]
From the information given
The standard deviation σ = 136 dollars
The sample n = 45
Thus,
[tex]\sigma_{\bar{X}}=\frac{136}{\sqrt{45}}=\frac{136\sqrt{5}}{15} \approx 20.274[/tex]
The standard deviation for the sample mean distribution is [tex]\sigma_{\bar{X}}=\frac{136}{\sqrt{45}}=\frac{136\sqrt{5}}{15} \approx 20.274[/tex]
