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Z-Score and Percentile in Excel

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In determining automobile mileage ratings, it was found that the mpg in the city (x) for a certain model is normally distributed, with a mean of 24 mpg and a standard deviation of 1.0 mpg. Find the following:

a. P(X) < 25)
b. P(22 < X < 24)
c. P(X > 26)
d. P(X < 23)
e. The mileage rating that the upper 5% of cars achieve.

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Percentile rank and inter-quartile range: Example question

For a normally distributed test with a mean of 100 and standard deviation of 20:

a) What score would be associated with the 80th percentile?
b) What would the inter-quartile range be for the test?
c) What would be the percentile rank of a score of 125?

Please give detailed notes explaining the steps required to answer each of these questions.

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