Question

The Empirical Rule is based on the standardized normal distribution.

- Describe how you could use the Empirical Rule to evaluate the distribution of scores on a national test. You are given the following information for the national test: (1) the population mean = 450 and (2) the population SD = 75.
- Second, based on the information given above, estimate the range of scores on this test. That is, estimate the low score and the high score on the test. Discuss how you arrived at your estimate for each score.
- Finally, determine where students’ test scores on the national
test would place them in terms of their percentile ranking. You are
given the following information on test scores of three
students.

- Student A scored a 600. What percentile is this student?
- Student B scored a 225. What percentile is this student?

Let’s say a student’s score placed them in the 99th percentile. Estimate the student’s score using whatever means gives you a good estimate.

Answer #1

a)We will have to standardize the test scores and then calculate the probability of the students above and below the scores.

b)As the scores are distributed normally, we can assume the scores to bottom out at -3 and +3 Standard deviations.

c)The above scores would place the students at 0.13 percentile and 99.87 percentile

What is the empirical rule?
A rule for determining the average of a normal distribution
based on the standard deviation.
A rough estimate of how different the sample and population
means should be for the result to be statistically significant.
A guideline of how one should gather empirical data.
A calculation rule for the confidence interval.
None of these

A nationwide test taken by high school sophomores and juniors
has three sections, each scored on a scale of 20 to 80. In a recent
year, the national mean score for the writing section was 50.4,
with a standard deviation of 9.1. Based on this information,
complete the following statements about the distribution of the
scores on the writing section for the recent year.
A. According to chebyshev's theorem, at least____of the scores
lie between 23.1 and 77.7.
B. According...

Q1-. A normal distribution has a mean of 15 and a standard
deviation of 2. Find the value that corresponds to the 75th
percentile. Round your answer to two decimal places.
Q2-.Tyrell's SAT math score was in the 64th percentile. If all
SAT math scores are normally distributed with a mean of 500 and a
standard deviation of 100, what is Tyrell's math score? Round your
answer to the nearest whole number.
Q3-.Find the z-score that cuts off an area...

A nationwide test taken by high school sophomores and juniors
has three sections, each scored on a scale of 20 to 80 . In a
recent year, the national mean score for the writing section was
49.9 . Based on this information, complete the following statements
about the distribution of the scores on the writing section for the
recent year.
(a) According to Chebyshev's theorem, at least ?56%75%84%89% of
the scores lie within 2 standard deviations of the mean,
49.9...

2.
In the following questions, assume you have a normal
distribution.
The average score on a mathematics test is 36. The standard
deviation is 4.
What percentage can be expected to score between 33 and
35?
3. In the following questions, assume you have
a normal distribution.
The average score on a mathematics test is 36. The standard
deviation is 4.
What score falls at the 50th percentile?
4. Given, an IQ test with:
u= 100
o= 16
What percent...

a) Suppose we were not sure if the distribution of a population
was normal. In which of the following circumstances would we NOT be
safe using a t procedure?
A. A histogram of the data shows moderate
skewness.
B. The mean and median of the data are nearly
equal.
C. A stemplot of the data has a large
outlier.
D. The sample standard deviation is large.
(b) Which of the following is an example of a matched pairs
design?
A....

Q1-. A normal distribution has a mean of 15 and a standard
deviation of 2. Find the value that corresponds to the 75th
percentile. Round your answer to two decimal places.
Q2-.Tyrell's SAT math score was in the 64th percentile. If all
SAT math scores are normally distributed with a mean of 500 and a
standard deviation of 100, what is Tyrell's math score? Round your
answer to the nearest whole number.
Q3-.Find the z-score that cuts off an area...

PLEASE TYPE DO NOT WRITE THANK YOU!
The Graduate Record Examination (GRE) is a test required for
admission to many US graduate schools. Students’ scores on the
quantitative portion of the GRE follow a normal distribution with a
mean of 150 and a standard deviation of 8.8. In addition to other
qualifications, a score of at least 152 is required for admission
to a particular graduate school.
a )Determine the 80thpercentile of GRE scores.
b) Determine the GRE scores that...

You may need to use the appropriate technology to answer this
question.
A standardized exam consists of three parts: math, writing, and
critical reading. Sample data showing the math and writing scores
for a sample of 12 students who took the exam follow.
Student
Math
Writing
1
540
474
2
432
380
3
528
463
4
574
612
5
448
414
6
502
520
7
480
430
8
499
459
9
610
615
10
572
541
11
390
329
12...

Question1: It is known the population IQ score follows a normal
distribution with mean as 100, SD as 10. A researcher is interested
in studying if the average IQ of students from statistics courses
on average has a higher IQ score than the population IQ score. To
test this hypothesis, the researcher randomly collected a sample of
25 students from statistic class, the mean IQ score for this sample
is 110. Compete for the hypothesis test at significant level.
Step...

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