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Assume that on the third exam in a calculus course, the average score over the years has been 72 with a standard deviation 12.You are currently taking the course and there are 25 students in the class?
06 / 02 / 2025
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Given the following sample of 10 high
temperatures from March:55, 60, 57, 43,
59, 66, 72, 65, 59, 47.
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Determine
the mean.
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Determine the median.
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Determine the mode.
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Describe the shape of the distribution.
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Determine Q1, Q2, Q3 and IQR.
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The contingency table shows classification of
students in a Statistics class.
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From NJ
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From PA
|
|
GPA at least 3.0
|
15
|
5
|
20
|
GPA below 3.0
|
45
|
35
|
80
|
|
60
|
40
|
100
|
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If a student is selected at random, what is the
probability that he/she is from NJ?
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If a student is selected at random, what is the
probability that he/she has a GPA below 3.0?
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If we know that the student is from PA, what is
the probability that he/she has a GPA of at least 3.0?
-
If a student is selected at random, what is the
probability that he/she is from NJ and has a GPA below 3.0.
-
If a student is selected at random, what is the
probability that he/she from PA and has GPA of at least 3.0.
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Your friend is applying for 4 jobs.The hourly pay rate for the 4 jobs are, $8,
$12, $15, $20.The probability
distribution below shows the probability of getting each of these jobs:
Job Pay Rate,X
|
Probability, P(X)
|
8
|
.30
|
12
|
.20
|
15
|
.40
|
20
|
.10
|
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What is the probability that your friend will
get a job paying at least $15/hour?
-
What is the expected pay rate for your friend?
-
It is known that 31% of cars are considered gas
hogs (i.e. they give less than 15 mpg).
If we select 20 cars at random:
-
What is the probability that exactly 4 will be
gas hogs?
-
What is the probability the at least 4 but not
more than 7 will be gas hogs?
-
How many cars are most likely to be gas hogs?
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You ask all 200 students at school how much
money they have in their pockets.The
amount ranges from $0 to $130.You determine
the mean to be $56.40 with standard deviation of $8.40.You believe that the amount is normally
distributed.
-
If you pick a person at random, what is the
probability that he/she has at least $45?
-
What percentage of the students will have
between $40 and $50 in their pockets.
-
If you pick a person at random, what is the
probability that he/she has either less than $30 or more than $70.
-
Approximately how many people in the class do
you expect to have at least $65?
-
We want to identify the students with top 10.5%
amounts as “rich”.What is the minimum
dollar amount the students in this group would need in their pockets.
-
Assume that on the third exam in a calculus
course, the average score over the years has been 72 with a standard deviation
12.You are currently taking the course
and there are 25 students in the class?
- What is the probability that
the mean score for your class will be greater than 75?
- What is the probability that
the mean score for your class will be between 68 and 70?
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A sample of 25 days in summer yields an average
high temperature of 80 with a standard deviation of 12.
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Give a point estimate of the true mean of the
high temperature.
-
Find a 99% confidence interval for the average
high temperature for the summer.
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How big a sample do we need if we want to be 90%
confident of being within 7 degrees of the population mean?
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A sample of 100 exams yielded an average grade
of 82 and standard deviation of 14.Find
a 95% confidence interval for the average exam grade.
-
Heights of aliens from Mars are known to be
normally distributed with a population standard deviation of 9 inches.How big a sample do we need to take if we
want be 95% confident that our error will not exceed 3 inches?
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Preliminary studies have shown that 20% of the
voters might be willing to vote for Sran for President.
-
Construct a 90% confidence interval for the
proportion of voters who would be willing to support Sran.
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Before entering the race, Sran would like to conduct
a poll to check his level of support.How
big should be the sample be if he wants to be 95% sure that the error is no
more than 2%?
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The average weight of men joining a gym has
historically been 170 pounds with a standard deviation of 27.The owner feels that the average weight has
now decreased to less than 165 pounds.
To support his claim, the owner conducts a sample of 25 men and finds
their average to be 153.He would like
to use a significance level of .05 to test his claim.
-
State the null hypothesis.
-
State the alternate hypothesis.
-
Will you use z or t distribution for this
problem?
-
Is this a two-tail test or a one-tail test?Draw a normal curve representing the problem.
-
Determine the critical value.
-
Determine the rejection region.
-
Calculate the test statistic.
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Would you accept or reject the owner’s
claim?Explain.
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The average score on a certain college entrance
test has been known to be 240.The dean
of a university feels that this has changed.
He conducts a sample of 25 students to test his claim.The sample yields an average of 232 with a
standard deviation of 25. He would like to use a significance level of .10.
-
State the null hypothesis.
-
State the alternate hypothesis.
-
Will you use z or t distribution for this
problem?
-
Is this a two-tail test or a one-tail test?Draw a normal curve representing the problem.
-
Determine the critical value.
-
Determine the rejection region.
-
Calculate the test statistic.
-
Would you accept or reject the dean’s claim?
-
A presidential candidate states that she
currently has exactly 30% of the vote.A
newspaper thinks that this number is inaccurate.So it conducts a sample 500 voters and finds 175
people support the candidate.The
newspaper would like to test its claim using .05 significance level.
-
State the null hypothesis.
-
State the alternate hypothesis.
-
Will you use z or t distribution for this
problem?
-
Is this a two-tail test or a one-tail test?Draw a normal curve representing the problem.
-
Determine the critical value.
-
Determine the rejection region.
-
Calculate the test statistic.
-
Would you accept or reject the newspaper’s
claim?