anonymous
  • anonymous
According to records, the amount of precipitation in a certain city on a November day has a mean of .1 inches, with a standard deviation of .6 inches. What is the probability that the mean daily precipitation will be .098 inches or more for a random sample of 40 November days (taken over many years)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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DebbieG
  • DebbieG
This is asking about a probability related to a SAMPLE MEAN, not just a data value. Thuse, you need to use the Central Limit Theorem formula to get the z-score: \[\large z=\frac{ \bar{x} -\mu}{ \frac{ \sigma }{ \sqrt{n}} }\] You have \[\bar{x}=0.098\]\[\mu=0.1\]\[\sigma=0.6\]and n = 40. Compute the z-score, then use a normal table (or a calculator) to find the area to the right of the z-score.
anonymous
  • anonymous
i get an answer of 0.021
anonymous
  • anonymous
wait thats just the z score right?

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DebbieG
  • DebbieG
Yes. And you should have gotten z=-0.021, since x-bar-0.021.
anonymous
  • anonymous
so on the calculator i would just do P(Z<=-.021) correct?
anonymous
  • anonymous
or would it be 1 - that?
DebbieG
  • DebbieG
What is the probability that the mean daily precipitation will be .098 inches OR MORE... so you want the P(Z>-0.021) ---- correct, you can get the area to the left, and subtract from 1. Or get the area to the right.
DebbieG
  • DebbieG
Or, if you understand how to take advantage of the symmetry of the distribution, you can even use P(Z<0.021) which is = P(Z>-0.021). :)
anonymous
  • anonymous
awesome I think i am following you

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