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More practice with Normal Curves and Percentiles
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Percentile Questions:
1. In a recent race Lightning McQueen placed
the rest ofthe racers?
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out of 45 racers. What was his percentile compared to
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There are 14,000 students competing in the National Spelling Bee. You placed in the 53'd percentile.
How many students placed lower than you?
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3. Below is a stem-and-leaf plot for a recent test for two elasses. |enny scored an87. Answer the
following questions:
a) If fenny is in class A" then what is her percentile
when only looking at class A?
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b) If |enny is in class B, then what is her percentile
when only looking at class B?
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c) If both class scores are combined, then
what is fenny's percentile?
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6
Normal Curve
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Questions.
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4, It is known
that when a specific type of radish is grown in a certain manner without fertilizer the
weights of the radishes produced are normally distributed with a mean of 40g and a standard deviation
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(a) Wlerprspp4r-on
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(b) What proportion oi radishei weighs more than 519?
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(c) What proportion of radishes weighs between 35gand 47g?
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[d] If a farmer grew 2000 radishes, how manywould weigh more than 45g?
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(e) 30% of radishes weigh more than how many grams?
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(0 The middl e 600/o of all radishes welgh between what two values?
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(g) What is the 80tr percentile of radiih weights?
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A bottle-filling machine fills bottles every day with a mean of 20,000 bottles and a standard deviation
of 2,000 bottles. Assume that the production is normally distributed.
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(a) What proportion of days had more than 21,500 bottles filled?
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[b] What proportion of days had less than 17,100 bottles filled?
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(c) What proportion of days had between 19,000 and 21,300 bottles filled?
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(d) If a year contains 255 working d4ys, how many days had more than 19,000 bottles
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filled?
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(e) The middle
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of all days filled between what two numbers of bottles?
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(f) what is the 25s percentile for number of bottles filled in a day?
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(g) What is the 75tr percentile for number of bottles filled in a day?
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(h) Suppose that one day they were able to fill 25,360 bottles!
Is this an
outlier? fustiff your'response.
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6. Most graduate schools of business- require applicants for admission to take the Graduate Management
Admission Council's GMAT examination. Scores on the GMAT are approximately normally distributed
with a mean of 527 and a standard deviation of tLZ.
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(a) What proportion of test takers score above a 500 on the GMAT?
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[b] How high must an individual
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score on the GMAT in order to score in the highest 5%?
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(c) What is the 90tr percentile of all GMAT scores?
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(d) The middle
B0o/o
of all test takers score between what two GMAT scores?
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7. The average number of acres burned by forest and range fires in a large New Mexico county is 4,300
of acres burned
acres p", y.ui, with a standard deviation of ZSO acres. The distribution of the number
per year is Normal.
(a) What proportion of years will have between 2,500 and 4,200 acres burned from forest and range
fires?
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(b) What number of burnt acres corresponds to the 38tt'percentile?
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(c) Suppose records have been kept for the past 175 years. How many years had over 3,900 acres
burned?
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(d) The middle
25o/o
ofall years had between how many acres burned?
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