# Statistics: Percentile Rank

A survey of college students was conducted during final exam week to assess the number of cups of coffee consumed each day. The mean number of cups was 5 with a standard deviation of 1.5 cups. The distribution was normal.

A. What proportion of students drank 7 or more cups of coffee per day?

B. What proportion of students drank 2 or more cups of coffee per day?

C. What proportion of students drank between 2 and 7 cups of coffee per day?

D. How many cups of coffee would an individual at the 60th percentile rank drink?

E. What is the percentile rank for an individual who drinks 4 cups of coffee a day?

F. What is the percentile rank for an individual who drinks 7.5 cups of coffee a day?

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1. A, B, C, E, F. Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores.

D, E, F. Percentile rank is proportion ≤ that score.

For D, start with the table to get the Z score, then use the above equation.

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2. All it has in the back of my textbook is Appendix A where it states, "Areas Under the Normal Curve (Z-Table)." Is this the correct table and what exactly am I supposed to look for? There are no straight numbers because on this table is just numbers that are in decimals. The table doesn't have straight numbers such as 1, 2, 3, 4, 5, 6, etc.

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3. A survey of college students was conducted during final exam week to assess the number of cups of coffee consumed each day. The mean number of cups was 5 with a standard deviation of 1.5 cups. The distribution was normal.

A. What proportion of students drank 7 or more cups of coffee per day?

B. What proportion of students drank 2 or more cups of coffee per day?

C. What proportion of students drank between 2 and 7 cups of coffee per day?

D. How many cups of coffee would an individual at the 60th percentile rank drink?

E. What is the percentile rank for an individual who drinks 4 cups of coffee a day?

F. What is the percentile rank for an individual who drinks 7.5 cups of coffee a day?

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4. vnvn

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