Question
Asked Nov 9, 2019
1 views

77% of all students at a college still need to take another math class. If 5 students are randomly selected, find the probability that

a. Exactly 2 of them need to take another math class. 
b. At most 2 of them need to take another math class. 
c. At least 3 of them need to take another math class.

Round all answers to 4 decimal places.

check_circle

Expert Answer

Step 1

Binomial distribution:

The binomial distribution gives the probability of number of successes out of n trials in a series of Bernoulli trials.

The probability mass function (pmf) of a binomial random variable X is given as:

help_outline

Image Transcriptionclose

п |р'а, х3D0,1,..., п;0 <р<1;q %3D1-р Р(x -х)-()Pig otherwise

fullscreen
Step 2

a.Computing the probability that exactly 2 of them need to take another math class:

It is given that 77% of the students need to take another math class.

A sample of 5 students is selected.

Thus, n = 5 and p = 0.77.

Define the random variable X as the number of students needs to take another math class.

The probability that exactly 2 of them need to take another math class is obtained as follows:

help_outline

Image Transcriptionclose

Using the EXCEL formula, P(X 2) 0.0721 =BINOM.DIST(2,5,0.77,0)

fullscreen
Step 3

b.Computing the probability that at most 2 of them need to take another math class:

The probability t...

help_outline

Image Transcriptionclose

Using the EXCEL formula, =BINOM.DIST (2,5,0.77,1) P(X 2) 0.0836|

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as ...

A: Hey, since multiple questions are posted, we will answer first three subparts of first question acco...

question_answer

Q: rosoft Edge atic/nb/ui/evo/index.html?deploymentid-589573205424674386703380718elSBN-9780357035108&id...

A: Given Datadfbetween = 2dfwithin = 30Degrees of freedom of treatments is given byK-1 = 2K represents ...

question_answer

Q: Test the given claims using the traditional method of hypothesis testing.   Various temperature meas...

A: The hypotheses for the test is given below:Null hypothesis:H0: µ = 22.Alternative hypothesis:H1: µ ≠...

question_answer

Q: Please help me with this problem

A: Given dataSample size(n) = 144Sample mean = 18Population standard deviation = 2.9Significance level(...

question_answer

Q: Please help me with this problem

A: Given dataSample size(n) = 27Sample mean = 76.2Population standard deviation = 21.4Significance leve...

question_answer

Q: Given that a distribution on a test has a mean of 70 and a standard deviation of 12 A.  Find the pro...

A: Central Limit Theorem for mean:If a random sample of size n is taken from a population having mean µ...

question_answer

Q: A population has a mean of 75 and a standard deviation of 15. You randomly sample nine people from t...

A: From the given information, the population has a mean of 75 and a standard deviation of 15. And the ...

question_answer

Q: Today, the waves are crashing onto the beach every 5.3 seconds. The times from when a person arrives...

A: Let X be random variable uniformly distributed between 0 and 5.3 seconds.Denote X as the time from a...

question_answer

Q: A population of values has a normal distribution with μ=179 and σ=98.2. You intend to draw a random ...

A: The provided information are:Population mean (µ) = 179.Population standard deviation (σ) = 98.2Sampl...