I dont' really understand this question.
The construction industry has determined that the average time to construct a two floor, family house in Westchester County, New York takes 85 days -- with a deviation of 10 days. Mr. Cox wants to purchase a new home in Westchester County, but his builder has just instructed him that his houses may take 106 days. Mr. Cox's bankers/lenders will guarantee him $400k if his Z-score(based upon a 106 day completion) is normal. (that's the hint) Does Mr. Cox receive the money? Explain.
Could anyone help me out with this please? I'm not sure how to answer this question.
average mean (mu aka, mean from which score X was obtained) = 85
sigma (standard deviation of normal distribution from which X was obtained) = 10
estimated mean (X aka, raw score) = 106
z(obs) = (X - mu)/sigma
z(obs) = (106 - 85)/10
z(obs) = 2.1
check +2.1 in z-score table (which should be in the back of your book) to see if percentile is normal. :) good luck
Thanks!
To answer the question, we need to calculate the Z-score and check it in a Z-score table to determine if it falls within the normal range.
1. Calculate the Z-score:
The formula for calculating the Z-score is:
Z(obs) = (X - mu) / sigma
Given:
average mean (mu) = 85
standard deviation (sigma) = 10
estimated mean (X) = 106
Substituting the values into the formula, we get:
Z(obs) = (106 - 85) / 10
Z(obs) = 2.1
2. Check the Z-score:
To determine if the Z-score of 2.1 falls within the normal range, we need to consult a Z-score table. These tables can typically be found in the back of textbooks or online.
Look up the Z-score of 2.1 in the table and find the corresponding percentile. The percentile represents the proportion of values within the normal range.
If the percentile is within an acceptable range, we can conclude that Mr. Cox receives the $400k.
Good luck with your search for the Z-score table!