Question

Suppose a college math scores are approximately normally distributed with mean μ=70 and standard deviation σ=10.

a. What score should a student aim to receive to be in the 95th percentile of the math scores?

b. You took a random sample of 25 students from this population. What is the probability that the average score in the sample will be equal to or greater than 75?

Answer #1

Suppose Students’ scores on the SAT are normally distributed
with μ= 1509 and σ= 321
A) What percentage of a students score less than 1188? (An
approximate answer is fine here)
B) What percentage of a students score between 867 and 2151? (An
approximate answer is fine here)
C) Find the probability of a student scoring more than 1600

Class scores are normally distributed with a μ= 100 and σ =
16
a) If a student has a score of 125, what percentage of students
have higher scores?
Draw the curve and decide where the Z score falls on it.
b) If a student has a score of 90, what percentage of students
have higher scores?
Draw the curve and decide where the Z score falls on it.

In a normal distribution, μ = 1400 and σ = 90. Approximately,
what percentage of scores lie between 1310 and 1445?
In a population of normally distributed scores, μ = 70 and σ =
24. Approximately what percentage of random samples of 36 scores
would have means with a value in the range 64 to 76?

Eleanor scores 680 on the math portion of the SAT. The
distribution of math SAT scores is approximately Normal, with mean
500 and standard deviation 100. Jacob takes the ACT math test and
scores 27. ACT math test scores are Normally distributed with mean
18 and standard deviation 6.
a. Find the standardized scores (z-scores) for both students.
b. Assuming that both tests measure the same kind of ability, who
has the higher score?
c. What score must a student...

Assume that statistics scores that are normally distributed with
a mean 75 and a standard deviation of 4.8 (a) Find the probability
that a randomly selected student has a score greater than 72. (b)
Find the probability that a randomly selected student has a score
between 70 and 80. (c) Find the statistics score separating the
bottom 99.5% from the top 0.5%. (d) Find the statistics score
separating the top 64.8% from the others.

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
their mean Math score is more than 520. You MUST show what went
into the calculator along with your final answer rounded correctly
to 3 significant decimal places.

Algebra scores in a school district are approximately normally
distributed with mean μ = 72 and standard deviation σ = 5. A new
teaching-and-learning system, designed to increase average scores,
is introduced to a random sample of 36 students, and in the first
year the average was 73.5.
(a) What is the probability that an average as high as 73.5
would have been obtained under the old system?
(b) Is the test significant at the 0.05 level? What about the...

Algebra scores in a school district are approximately normally
distributed with mean μ = 72 and standard deviation σ = 5. A new
teaching-and-learning system, designed to increase average scores,
is introduced to a random sample of 36 students, and in the first
year the average was 73.5.
(a) What is the probability that an average as high as 73.5
would have been obtained under the old system?
(b) Is the test significant at the 0.05 level? What about the...

Suppose the scores on a reading ability test are normally
distributed with a mean of 65 and a standard deviation of 8.
A) If one student is chosen at random, what is the probability
that the student's score is greater than 81 points"?
B) If 500 students took the reading ability test HOW MANY
students would expect to earn a score greater than 81 points?
c) Find the probability of randomly selecting 35 students (all
from the same class) that...

The score on Math 206 class X, is normally distributed with
μ=74.5 and σ=8.7.
Assume for the sake of this problem that the score is a continuous
variable.
(a) Write the event ''a score equal to 64.5'' in terms of
X: .
(b) Find the probability of this event:
(c) Find the probability that a randomly chosen score is greater
than 84.5: .
(d) Find the probability that a randomly chosen score is between
64.5 and 84.5: .

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