Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Using the normal distribution and the central limit theorem, it is found that there is a 0.6328 = 63.28% probability that a random sample of 100 accounting graduates will provide an average that is within $902 of the population mean.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
Hence, the probability of sample having mean within M of the population mean is the p-value of [tex]Z = \frac{M}{\frac{\sigma}{\sqrt{n}}}[/tex] subtracted by the p-value of [tex]Z = -\frac{M}{\frac{\sigma}{\sqrt{n}}}[/tex].
In this problem, we suppose [tex]\sigma = 10000[/tex], and thus, with a sample of 100, we have that [tex]s = \frac{10000}{\sqrt{100}} = 1000[/tex].
- Within $902, hence [tex]M = 902[/tex].
[tex]Z = \frac{M}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{902}{1000}[/tex]
[tex]Z = 0.902[/tex]
[tex]Z = 0.902[/tex] has a p-value of 0.8164.
[tex]Z = \frac{M}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = -\frac{902}{1000}[/tex]
[tex]Z = -0.902[/tex]
[tex]Z = -0.902[/tex] has a p-value of 0.1836.
0.8164 - 0.1836 = 0.6328.
0.6328 = 63.28% probability that a random sample of 100 accounting graduates will provide an average that is within $902 of the population mean.
A similar problem is given at https://brainly.com/question/24663213
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
