Question 1184669: An automotive engineer wants to estimate the cost of repairing a car that experience a 25 MPH head-on collision. He crashes 24 cars, and the average repair is $11,000. The standard deviation of the 24-car sample is $2,500.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the mean of the sample is 11000
the standard deviation of the sample is 2500
the sample size is 24.
the standard error = standard deviation divide by square root of sample size = 2500 / sqrt(24) = 510.3, rounded to one decimal place.
at 5% significance level, the confidence interval will contain 95% of the area under the normal distribution curve.
the critical z-score for that will be plus or minus 1.96.
your critical raw scores will be based on the z-score formula of:
z = (x - m) / s
for the low z-score, the formula becomes:
-1.96 = (x - 11000) / 510.3.
solve for x to get:
x = -1.96 * 510.3 + 11000 = 9999.8.
for the high z-score, the formula becomes:
1.96 = (x - 11000) / 510.3.
solve for x to get:
x = 1.96 * 510.3 + 11000 = 12000.188.
x, in this case, represents the population mean which is assumed to be between 10,000 and 12,000 at 5% significance level.
i'm not sure if this is what you are looking for, but i couldn't see anything else you might want to find.
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