Question

Problem 7: The 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?

Answer #1

The scores of individual students on the American College
Testing (ACT) program composite college entrance examination have a
normal distribution with mean 18.6 and standard deviation 6.0.
Forty-nine randomly selected seniors take the ACT test. What is the
probability that their mean score is less than 18? Round your
answer to 4 decimal places.

The scores of individual students on the American College
Testing (ACT) composite college entrance examination have a normal
distribution with mean 19.2 and standard deviation 6.8. (a) What is
the probability that a single student randomly chosen from all
those taking the test scores 24 or higher? 0.2389 Correct: Your
answer is correct. (b) Now take an SRS of 69 students who took the
test. What are the mean and standard deviation of the average
(sample mean) score for the...

The scores of students on the ACT college entrance examination
in a recent year had a normal distribution with mean 24 and
standard deviation 4. What ACT score should a student have in order
to be in the top 5% of test takers? (use 3 decimals)

A sample of 16 students took the American College Testing (ACT)
Program composite college entrance exam and were found to have a
mean of 18 and a sample SD equal to 6. (A) What is the value of the
estimated standard error of the mean (SEM)? (B) Provide an
interpretation of the value obtained in part A. (C) Describe how
the researcher might reduce the size of the SEM if the study is
repeated.

(1 point) The scores of a college entrance examination had a
normal distribution with mean μ=550.6μ=550.6 and standard deviation
σ=25.6σ=25.6.
(a) What is the probability that a single student randomly
chosen from all those who took the test had a score of 555 or
higher?
ANSWER:
For parts (b) through (d), consider a simple random sample of 35
students who took the test.
(b) The mean of the sampling distribution of x¯x¯ is:
The standard deviation of the sampling distribution...

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...

The scores of students on the SAT college entrance examinations
at a certain high school had a normal distribution with mean
?=531.7 and standard deviation ?=25.5
consider a simple random sample (SRS) of 30 students who took
the test.
The standard deviation of the sampling distribution for ?¯
is?
What is the probability that the mean score ?¯ of these students
is 536 or higher?

There are two major tests of readiness for college, the ACT and
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distribution of ACT scores for more than 1 million students in a
recent high school graduating class was roughly normal with mean μ
= 20.8 and standard deviation σ = 4.8. SAT scores are reported on a
scale from 400 to 1600. The SAT scores for 1.4 million students in
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The scores on the SAT college entrance exam are normally
distributed with a mean Math score of 480 and a standard deviation
of 100. If you select 50 students, what is the probability that
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to 3 significant decimal places.

A study considers whether the mean score of a college entrance
exam for students in 2019 (Group 1) was higher than the mean score
in 2018 (Group 2). A random sample of 25 students who took the exam
in 2019 and a random sample of 25 students who took the exam in
2018 were selected. Assume α=0.1. If the p-value is 0.34, which is
the following is an accurate interpretation?
(a) At α=10%, there is sufficient evidence to indicate that...

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