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AP Statistics
YMM Chapter 2.2
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NOTE: You MUST draw a normal curve (you may use the template provided) and
shade the appropriate regions to get credit for the problems!!!!!!!
1. Professors’ GradesSuppose that you are deciding whether to take Professor
Fisher’s class of Professor Savage’s next semester. You happen to know that each
professor gives A’s to those scoring above 90 on the final exam and F’s to those
scoring below 60. You also happen to know that the distribution of scores on
Professor Fisher’s final is approximately normal with mean 74 and standard
deviation 7 and that the distribution of scores on Professor Savage’s final is
approximately normal with mean 78 and standard deviation 18.
a.) Produce a sketch of both teachers’ grade distribution (two pictures)
b.) Which professor gives the higher proportion of A’s? Show the appropriate
picture and calculations to support your answer.
c.) Which professor gives the higher proportion of F’s? Show the appropriate
picture and calculations to support your answer.
d.) Suppose that Professor DeGroot has a policy of giving A’s to the top 10% of
the scores on his final, regardless of the actual scores. If the distribution
of scores on his final turns out to be normal with mean 69 and standard
deviation 9, how high does your score have to be to earn an A?
2. Professors’ Grades (cont) Suppose that Professors Wells and Zeddes have final
exam scores that are approximately normally distributed with mean 75. the
standard deviation of Wells’s scores is 10, and that of Zeddes’s scores is 5
a.) With which professor is a score of 90 more impressive? Support your
answer with appropriate probability calculations and with a sketch.
b.) With which professor is a score of 60 more discouraging? Support your
answer with appropriate probability calculations and with a sketch.
3. IQ Scores: Suppose that the IQ scores of students at a certain college follow a
normal distribution with mean 115 and standard deviation 12.
a.) What proportion of the students have an IQ below 100?
b.) Find the proportion of these undergraduates having IQs greater than 130
c.) Find the proportion of these undergraduates having IQs between 110 and
130.
d.) With his IQ of 75, Forrest Gump would have a higher IQ than what
percentage of these undergraduates?
e.) Determine how high one’s IQ must be to be in the top 1% of all IQs at this
college
AP Statistics
YMM Chapter 2.2
Name:
Date:
4. Candy Bar Weights Suppose that the wrapper of a certain candy bar lists its
weight as 2.13 ounces. Naturally; the weights of individual bars vary somewhat.
Suppose that the weights of these candy bars vary according to a normal
distribution with mean of 2.2 ounces and standard deviation of .04 ounces.
a.) What proportion of candy bars weigh less than the advertised weight?
b.) What proportion of candy bars weigh more than 2.25 ounces?
c.) What proportion of candy bars weigh between 2.2 and 2.3 ounces?
d.) If the manufacturer wants to adjust the production process so that only 1
candy bar in 1000 weighs less than the advertised weight, what should the
mean of the actual weights be (assuming that the standard deviation of the
weights remains .04 ounces)?
e.) If the manufacturer wants to adjust the production process so that the
mean remains at 2.2 ounces but only 1 candy bar in 1000 weighs less than
the advertised weight, how small does the standard deviation of the weights
need to be?
f.) If the manufacturer wants to adjust the production process so that the
mean is reduced to 2.15 ounces but only 1 candy bar in 1000 weighs less than
the advertised weight, how small does the standard deviation of the weights
need to be?
5. SATs and ACTs: Suppose that a college admissions office needs to compare
scores of students who take the Scholastic Aptitude Test (SAT) with those who
take the American College Test (ACT). Suppose that the scores for college
applicants who take the SAT have mean of 896 and a standard deviation of 174.
Further, suppose that scores among the college’s applicants who take the ACT have
a mean of 20.6 and a standard deviation of 5.2. Consider applicant Bobby, who
scored 1080 on the SAT, and applicant Kathy, who scored 28 on the ACT.
a.) Assuming that SAT scores of the college’s applicants are normally
distributed, what proportion of applicants score higher than Bobby on the
SATs?
b.) Assuming that ACT scores of the college’s applicants are normally
distributed, what proportion of applicants score higher than Kathy on the
ACTs?
c.) Which applicant seems to be the stronger in terms of standardized test
performance?
EXTRA CREDIT: We looked at three baseball players and compared their batting
averages relative to the distribution of their decade. Find a major league baseball player
whose batting average seems to be comparable to these baseball greats. Find the mean
and standard deviation for the decade in which your player played and then compare that
player to the ones we investigated in class.