For the following questions, consider a data set that exhibits a normal distribu

Question

For the following questions, consider a data set that exhibits a normal distribution. Report the answers to the nearest 0.01. What is the Z score for the value that is larger than 12.3% of the data? What is the Z score for the value that is smaller than 1.1% of the data? Consider a portion of the data bounded above and below by certain Z scores. If we consider a region bounded below by Z = 0.4, what is the Z score of the upper bound if the region contains 6 7% of the data? Consider a set of 800 of normally distributed data values with a mean of 26 and a standard deviation of 4.0 How many values are larger than 27.00 (report answer to the nearest integer) How many values are between 23.00 and 28.00? (report answer to the nearest integer) What is your best estimate for the value of Q_3? (report answer to the nearest 0.01) Imagine that we take a sample from a population of interest. Sample data For the following questions use the sample values to the right: Assume that this sample accurately reflects the mean and standard 19 18 deviation of the population so you can use the normal distribution and Z scores for the problems below. (If you've read ahead in your book or lab manual you know we should really use t scores, don't worry about this right now, use the Z scores) Assuming that the population data is normally distributed, what is the value that you expect 67% of the data in the population to be smaller than? (round to nearest 0.01) What is your best estimate for the IQR of the population data? (round to nearest 0.01)

Explanation / Answer

Q2)

Part a:

P ( Z > z ) = 12.3% = 0.123

By using Normal Distribution Table we get

P ( Z > 1.16 ) = 0.123

Answer: 1.16

Part b:

P ( Z < z ) = 1.1% = 0.011

By using Norma l Distribution Table we get,

P ( Z < -2.29 ) = 0.011

Answer: -2.29

Part c:

P ( 0.4 < z < a ) = 6.7% = 0.067

P ( z < 0.4 ) = 0.6544

So from let the total area is 0.6544 + 0.067 = 0.7224

P ( Z < a ) = 0.7224

By using Norma l Distribution Table we get,

P ( Z < 0.59 ) = 0.7224

Answer: 0.7224

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