1 A normal distribution has a mean of µ = 18 with s = 4. Find score (X) needed to be in the bottom 29% of the distribution. Be sure to illustrate the normal distribution and shade in the region in question. 2) For a normal population with mean = 200 and population standard deviation = 25 find the probability of obtaining a sample mean greater than 188 for a sample of n = 20 scores? Be sure to illustrate the normal distribution and shade in the region in question.

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Asked Nov 6, 2019

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1 A normal distribution has a mean of µ = 18 with s = 4. Find score (X) needed to be in the bottom 29% of the distribution. Be sure to illustrate the normal distribution and shade in the region in question.

2) For a normal population with mean = 200 and population standard deviation = 25 find the probability of obtaining a sample mean greater than 188 for a sample of n = 20 scores? Be sure to illustrate the normal distribution and shade in the region in question.

Expert Answer

Step 1

Here, μX̅ = 18, s = 4.

The score (x) below which, 29% of the observations lie is such that:

P (X < x) = 0.29.

Using the Excel formula =NORM.INV(0.29,18,4), P (X < 15.79) = 0.29.

Thus, the...

Image Transcription
Distribution Plot Normal, Mean=18, StDev 4 0.10 008 006 004 029 0.02 000 15.79 18 х Density

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