Question

A survey reports that 65% of college students use Google as their search engine. If 100 students of a college were randomly selected and were asked whether he or she uses Google as their search engine. Using normal approximation to probability, what is the probability (with correction for continuity) that more than 65 will say yes?

Answer #1

A survey reports that 53% of college students use Google as
their search engine. If 100 students of a college were randomly
selected and were asked whether he or she uses Google as their
search engine. Using normal approximation to probability, what is
the probability (with correction for continuity) that at least 66
will say yes?

At a certain college in Louisiana, it is claimed that 77% of
the students at the college are receiving some form of student
tuition assistance. If 510 students at this college are randomly
selected, use the Normal approximation to binomial distribution to
find the probability that 370 or more of the students are receiving
some form of tuition assistance. (Hint: Remember to make the
continuity correction)

Suppose 5% of college students don’t use social media. We
randomly sampled 1000 college students.
a. Let X denote the number of students who don’t use social
media in this sample. Calculate the expected value and the standard
deviation for X.
b. Find the probability of observing 50 or less students who
don’t use social media in this sample. If you would like to use
normal approximation for binomial distribution, make sure to check
the conditions and you don’t need...

Suppose 5% of college students don’t use social media. We
randomly sampled 1000 college students. Let X denote the number of
students who don’t use social media in this sample. Calculate the
expected value and the standard deviation for X. Find the
probability of observing 50 or less students who don’t use social
media in this sample. If you would like to use normal approximation
for binomial distribution, make sure to check the conditions and
you don’t need to do...

Suppose 5% of college students don’t use social media. We
randomly sampled 1000 college students.
Let X denote the number of students who don’t use social media
in this sample. Calculate the expected value and
the standard deviation for X. (4 pts)
Find the probability of observing 50 or less students who don’t
use social media in this sample. If you would like to use normal
approximation for binomial distribution, make sure to check
the conditions and you don’t need...

Among students at a particular university, 90% have visited the
main dining hall at least once. What is the probability that of 100
randomly selected students, between 90-93 of them will have visited
the main dining hall at least once?
Answer this question using the binomial distribution.
Approximate this answer using the normal distribution without
the continuity correction.
Approximate this answer using the normal distribution and the
continuity correction. (Take note of how close your approximation
is.)

In a survey, 150 high school students were asked whether they
play sports. The survey also recorded the grade of each of the
participants. The responses are given below: Yes No Freshman 19 22
Sophomore 23 17 Junior 18 12 Senior 20 19 Use this table to
determine each of the following probabilities. Write each answer as
a percent rounded to one decimal place, i.e. 16.8%. Do not include
the percent symbol.
a) Find the probability that a randomly selected...

In a survey on study habits, students at a local
college were asked whether they listened to music while studying.
The following table was constructed.
Listens to Music
Does Not Listen to Music
Male
42
24
Female
5
47
Find the probability that a randomly selected student
is female or does not listen to music while studying.
Write only a number a your answer. Round to two
decimal places (for example: 0.73). Do not write as a percentage.

Consider the probability that more than 66 out of 125 students
will not pass their college placement test. Assume the probability
that a given student will not pass their college placement test is
1%. Specify whether the normal curve can be used as an
approximation to the binomial probability by verifying the
necessary conditions. Yes or No?

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...

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