Question

Scores for a common standardized college aptitude test are normally distributed with a mean of 506 and a standard deviation of 102. Randomly selected men are given a Prepartion Course before taking this test. Assume, for sake of argument, that the Preparation Course has no effect on people's test scores. If 1 of the men is randomly selected, find the probability that his score is at least 544.2. P(X > 544.2) = Enter your answer as a number accurate to 4 decimal places. If 14 of the men are randomly selected, find the probability that their mean score is at least 544.2. P(x-bar > 544.2) = Enter your answer as a number accurate to 4 decimal places. If the random sample of 14 men does result in a mean score of 544.2, is there strong evidence to support a claim that the Preapartion Course is actually effective? (Use the criteria that "unusual" events have a probability of less than 5%.)

No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 544.2 if the Preparation Course has no effect. Yes. The probability indicates that is is highly unlikely that by chance, a randomly selected group of students would get a mean as high as 544.2 if the Preparation Course has no effect.

Answer #1

µ = 506, σ = 102

a)

P(X > 544.2) =

= P( (X-µ)/σ > (544.2-506)/102)

= P(z > 0.3745)

= 1 - P(z < 0.3745)

Using excel function:

= 1 - NORM.S.DIST(0.3745, 1)

= **0.354**

b)

P(X̅ > 544.2) =

= P( (X̅-μ)/(σ/√n) > (544.2-506)/(102/√14) )

= P(z > 1.4013)

= 1 - P(z < 1.4013)

Using excel function:

= 1 - NORM.S.DIST(1.4013, 1)

= **0.0806**

c) Yes. The probability indicates that is is highly unlikely that by chance, a randomly selected group of students would get a mean as high as 544.2 if the Preparation Course has no effect.

Scores for a common standardized college aptitude test are
normally distributed with a mean of 484 and a standard deviation of
100. Randomly selected men are given a Prepartion Course before
taking this test. Assume, for sake of argument, that the
Preparation Course has no effect on people's test scores.
If 1 of the men is randomly selected, find the probability that his
score is at least 520.1.
P(X > 520.1) =
Enter your answer as a number accurate to...

Scores for a common standardized college aptitude test are
normally distributed with a mean of 490 and a standard deviation of
103. Randomly selected men are given a Test Preparation Course
before taking this test. Assume, for sake of argument, that the
test has no effect.
If 1 of the men is randomly selected, find the probability that
his score is at least 528.7. P(X > 528.7) = Enter your answer as
a number accurate to 4 decimal places.
If...

Scores for a common standardized college aptitude test are
normally distributed with a mean of 492 and a standard deviation of
100. Randomly selected men are given a Test Prepartion Course
before taking this test. Assume, for sake of argument, that the
test has no effect.
If 1 of the men is randomly selected, find the probability that
his score is at least 533.3. P(X > 533.3) = ?
Enter your answer as a number accurate to 4 decimal places....

Scores for a common standardized college aptitude test are
normally distributed with a mean of 503 and a standard deviation of
110. Randomly selected men are given a Test Prepartion Course
before taking this test. Assume, for sake of argument, that the
test has no effect.
If 1 of the men is randomly selected, find the probability that his
score is at least 553.8.
P(X > 553.8) =
Enter your answer as a number accurate to 4 decimal places. NOTE:...

Scores for a common standardized college aptitude test are
normally distributed with a mean of 515 and a standard deviation of
110. Randomly selected students are given a Test Prepartion Course
before taking this test. Assume, for sake of argument, that the
course has no effect.
If 1 of the students is randomly selected, find the probability
that their score is at least 581.7.
P(X > 581.7) =
Enter your answer as a number accurate to 4 decimal places.
If...

Scores for a common standardized college aptitude test are
normally distributed with a mean of 510 and a standard deviation of
98. Randomly selected men are given a Test Preparation Course
before taking this test. Assume, for sake of argument, that the
preparation course has no effect.
If 1 of the men is randomly selected, find the probability that
his score is at least 588.4.
P(X > 588.4) =
If 9 of the men are randomly selected, find the probability...

Scores for a common standardized college aptitude test are
normally distributed with a mean of 493 and a standard deviation of
115. Randomly selected men are given a Test Preparation Course
before taking this test. Assume, for sake of argument, that the
preparation course has no effect.
If 1 of the men is randomly selected, find the probability that his
score is at least 545.2.
P(X > 545.2) =
Answer as a number accurate to 4 decimal places.
If 14...

Scores for a common standardized college aptitude test are
normally distributed with a mean of 499 and a standard deviation of
97. Randomly selected men are given a Test Prepartion Course before
taking this test. Assume, for sake of argument, that the test has
no effect. If 1 of the men is randomly selected, find the
probability that his score is at least 557.2. P(X > 557.2) =
Enter your answer as a number accurate to 4 decimal places. NOTE:...

Scores for a common standardized college aptitude test are
normally distributed with a mean of 483 and a standard deviation of
101. Randomly selected men are given a Test Prepartion Course
before taking this test. Assume, for sake of argument, that the
test has no effect.
If 1 of the men is randomly selected, find the probability that his
score is at least 550.8.
P(X > 550.8) =
Enter your answer as a number accurate to 4 decimal places. NOTE:...

Scores for men on the verbal portion of the SAT-I test are
normally distributed with a mean of 509 and a standard deviation of
112.
(a) If 11 man is randomly selected, find the
probability that his score is at least 579.5
(b) If 13 men are randomly selected, find the
probability that their mean score is at least 579.5
13 randomly selected men were given a review course before taking
the SAT test. If their mean score is 579.5, is there...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 12 minutes ago

asked 25 minutes ago

asked 27 minutes ago

asked 32 minutes ago

asked 42 minutes ago

asked 45 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago