Question
In: Statistics and Probability
he scores of students on the ACT (American College Testing) college entrance examination in a recent...
he scores of students on the ACT (American College Testing) college entrance examination in a recent year had the normal distribution with mean μ = 18 and standard deviation σ = 6. 100 students are randomly selected from all who took the test.
a. What is the probability that the mean score for the 100 students is between 17 and 19 (including 17 and 19)?
b. A student is eligible for an honor program if his/her score is higher than 25. Find an approximation to the probability that at least 15 students of the 100 students are eligible for the honor program.
c. If the sample size is 4 (rather than 100), what is the probability that more than 50% (not include 50%) students are eligible for the honor program?
Solutions
orchestra answered 1 year agoRelated Solutions
The scores of students on the ACT (American College Testing)college entrance examination in a recent year...
The scores of students on the ACT (American College
Testing)college entrance examination in a recent year had the
normal distribution with meanμ= 18 and standard deviationσ= 6. 100
students are randomly selected from all who took the test
a.What is the probability that the mean score for the
100 students is between 17and 19 (including 17 and 19)?
b.A student is eligible for an honor program if his/her
score is higher than 25.Find an approximation to the probability
that at...
The scores of high school seniors on the ACT college entrance examination in a recent year...
The scores of high school seniors on the ACT college entrance
examination in a recent year had mean μ = 20.8 and
standard deviation σ = 4.8. 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 21 or higher?
(Round your answer to four decimal places.)
(b) Now take an SRS of 25 students who took the test. What are the
mean...
The composite scores of individual students on the ACT college entrance examination in 2009 followed a...
The composite scores of individual students on the ACT college
entrance examination in 2009 followed a normal distribution with
mean 21.1 and standard deviation 5.1.
What is the probability that a single student randomly chosen
from all those taking the test scores 23 or higher?
P( X >__?__ ) = P(z >__?__ ) =
____?__
What is the probability that a simple random sample of 50
students chosen from all those taking the test has an average score
of 23...
The ACT is a college entrance exam. ACT test scores follow a normal distribution with a...
The ACT is a college entrance exam. ACT test scores follow a
normal distribution with a mean of 22.2 points and a standard
deviation of 4.9 points. Let X = number of points scored on the
ACT. Answer the following questions.
A. Jasmine scored a 28.227 on the ACT. Calculate Jasmine's
Z-score.
B. Interpret Jasmine's z-score in terms of the problem.
C. What is the probability that a randomly selected individual
gets an ACT score that is lower than Jasmine's?...
Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of...
Scores on a certain nationwide college entrance examination
follow a normal distribution with a mean of 500 and a standard
deviation of 100. Find the probability that a student will
score...
a) over 650
b) less than 459
c) between 325 and 675
d) If a school only admits students who score over 680, what
proportion of the student's pool would be eligible for
admission?
e) what limit (score) would you set that makes the top 20% of
the students...
Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of...
Scores on a certain nationwide college entrance examination
follow a normal distribution with a mean of 500 and a standard
deviation of 100. Find the probability that a student will
score...
a) over 650
b) less than 459
c) between 325 and 675
d) If a school only admits students who score over 680, what
proportion of the student's pool would be eligible for
admission?
e) what limit (score) would you set that makes the top 20% of
the students...
The scores of students on the SAT college entrance examinations at a certain high school had...
The scores of students on the SAT college entrance examinations
at a certain high school had a normal distribution with mean μ=544
and standard deviation σ=29.1.
(a) What is the probability that a single student randomly
chosen from all those taking the test scores 548 or higher?
For parts (b) through (d), consider a simple random sample (SRS)
of 35 students who took the test.
(b) What are the mean and standard deviation of
the sample mean score x¯, of...
The scores of students on the SAT college entrance examinations at a certain high school had...
The scores of students on the SAT college entrance examinations
at a certain high school had a normal distribution with mean
?=545.8μ=545.8 and standard deviation ?=28.4σ=28.4.
(a) What is the probability that a single student, randomly
chosen from all those taking the test, would score 552 or
higher?
For parts (b) through (d), consider a simple random sample (SRS)
of 35 students who took the test.
(b) What are the mean and standard deviation of the sample mean
score ?¯x¯,...
The scores of students on the SAT college entrance examinations at a certain high school had...
The scores of students on the SAT college entrance examinations
at a certain high school had a normal distribution with
mean and standard deviation .
(a) What is the probability that a single student randomly
chosen from all those taking the test scores 545 or higher?
ANSWER:
For parts (b) through (d), consider a simple random sample (SRS) of
30 students who took the test.
(b) What are the mean and standard deviation of the sample mean
score , of 30...
The scores of students on the SAT college entrance examinations at a certain high school had...
The scores of students on the SAT college entrance examinations
at a certain high school had a normal distribution with mean
μ=535.4 and standard deviation σ=28.
(a) What is the probability that a single student randomly
chosen from all those taking the test scores 542 or higher?
ANSWER:
For parts (b) through (d), consider a simple random sample (SRS) of
25 students who took the test.
(b) What are the mean and standard deviation of the sample mean
score x,...
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