## z score problem

1. One series of tapestry from Persia, known as Ardabil rugs, was woven in a particular style during the 16th-17th Centuries in northwestern Iran. This style of rugs has a mean length of μ = 1.1 meters and a standard deviation of σ = 0.4 meters. A second series of tapestry, known as Sarabi rugs, was also woven during the same time at a nearby area has a mean length of μ = 1.5 meters and a standard deviation of σ = 0.5 meters. During the course of your excavations of a Medieval archaeological site in Iran, your field crew has unearthed a sample of tapestry that dates to the same time period and may represent one of these two styles. There are n = 11 tapestries in your sample, with a mean of [IMG]file:///C:/Users/Derek/AppData/Local/Temp/msohtml1/01/clip_image002.gif[/IMG]=1.4 meters. Calculate a z-score for your unknown sample twice, using the data provided for both styles of tapestry and answer the following questions.
A. What is the probability of finding a sample of Ardabil rugs with a mean length equal to or greater than that of your unknown sample?
B. What is the probability of finding a sample of Sarabi rugs with a mean length equal to or less than that of your unknown sample?
C. In your opinion, is it possible to assign your sample to one of these styles? Explain.
D. What are the effects on the standard errors of the mean and the z-scores of increasing the size of your unknown sample to N=20? Why should these values change with an increase in sample size?
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not sure how to set these problems up....like to calculate the two z scores do i use the mean of the unknown style as X?