Question

Let
X be the score on a national test of randomly selected student from
West High School and Y be the score on the same test of a randomly
selected student from East High School. Suppose X has a normal
distribution with mean 50 and variance 29. Y has a normal
distribution with mean 47 and variance 35, and X and Y are
independent. If a student from each high school is randomly
selected, what is the probability that the student from West high
school has a higher test score than the student from East high
school?

Answer #1

IQ scores are sometimes modeled as a continuous variable. Let X
be the IQ score of a student, to be randomly selected at a
University. Suppose that X has the normal distribution with a mean
of 110 and a standard deviation of 8.
a.) Find the probability that a randomly selected student has an
IQ higher than the national average of 100, but lower than 126.
b.) What IQ score has a probability of 0.01 of a randomly
selected student...

Suppose the random variable X records a randomly selected
student’s score on a national test, where the population
distribution for the score is normal with mean 70 and standard
deviation 5. A simple random sample of 200 students is taken.
(a) What is the distribution of the sample mean score? Is this
the exact distribution or an approximated distribution?
(b) What is the probability that the sample mean will exceed
71?
(c) What is the probability that the sample mean...

200 high school freshmen were randomly selected for a national
survey. Among the survey participants, the mean grade-point average
(GPA) was 2.7. If the data follows a normal distribution with a
standard deviation of 0.4, what is the margin of error, assuming a
95% confidence level?

QUESTION 7
Let x be a random variable representing the SAT math
score of student. We may assume that x has a normal
distribution and that the population standard deviation is 25. A
large university claims the average SAT math score for incoming
freshman is 650. You suspect that this claim is too high and decide
to test the claim. You select a random sample of 75 incoming
freshman and find the mean SAT math score to be 645. If
you...

A school district has four schools, six class in from each
school were randomly selected and the number of students in the
class were recorded. Test the claim that at least one school has a
different class size at a 0.01 level of significance.
School A
School B
School C
School D
44
43
37
30
45
50
33
32
49
40
35
35
47
40
32
25
29
47
40
31
32
31
33
29
The hypotheses for this...

) The mean ACT mathematics score for 60 randomly selected high
school students is 20.6. Assume the population standard deviation
is 5.4. The mean ACT science score for 75 other randomly selected
high school students is 20.8. Assume the population standard
deviation is 5.6. At ? = 0.01, can you reject the claim that the
ACT math and ACT science scores are equal? a.) Verify that 1.) Both
population standard deviations are known. _____ 2.) The samples
taken are random....

7. (10 pts.) The national mean score for the SAT is
910. An SAT preparation program claims that, on average, its
graduates score higher than the national average of 910. To test
the program’s claim, 36 students who have applied to take the SAT
are selected randomly for inclusion in the prep course.
anwsers must be in 4 decimal places
a. What are the hypotheses for the test?
b. Let X be the...

6.18 ACT scores of high school seniors. The
scores
of your state’s high school seniors on the ACT
college entrance examination in a recent year had
mean m 5 22.3 and standard deviation s 5 6.2. The
distribution of scores is only roughly Normal.
(a) What is the approximate probability that a single
student randomly chosen from all those taking the test
scores 27 or higher?(b) Now consider an SRS of 16 students who took
the
test. What are the...

Independent Samples T-TEST
Two rival schools, West Ridge College and East Ridge College,
each claim to have a better microbiology program than the
other. The microbiology students at both schools take
the same national exam at the end of the year. Although
West Ridge College gets a higher mean score, the East Ridge
College’s microbiology professor claims that the difference in
scores is too small to be statistically
significant. Here is the data
West Ridge College: Mean or =
85.8; 12.8; = 16
East Ridge College: Mean or =...

Let X be a randomly selected real number from the interval [0,
1]. Let Y be a randomly selected real number from the interval [X,
1].
a) Find the joint density function for X and Y.
b) Find the marginal density for Y.
c) Does E(Y) exist? Explain without calculation. Then find
E(Y).

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