1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anni [7]
3 years ago
14

A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 stude

nts registered for the course. (Round your answers to four decimal places.) (a) Compute the probability that 2 or fewer will withdraw. (b) Compute the probability that exactly 4 will withdraw. (c) Compute the probability that more than 3 will withdraw. (d) Compute the expected number of withdrawals.
Mathematics
1 answer:
Mkey [24]3 years ago
3 0

Answer:

(a) Probability that 2 or fewer will withdraw is 0.2061.

(b) Probability that exactly 4 will withdraw is 0.2182.

(c) Probability that more than 3 will withdraw is 0.5886.

(d) The expected number of withdrawals is 4.

Step-by-step explanation:

We are given that a university found that 20% of its students withdraw without completing the introductory statistics course.

Assume that 20 students registered for the course.

The above situation can be represented through binomial distribution;

P(X =r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,......

where, n = number of trials (samples) taken = 20 students

            r = number of success  

            p = probability of success which in our question is probability  

                  that students withdraw without completing the introductory  

                  statistics course, i.e; p = 20%

Let X = <u><em>Number of students withdraw without completing the introductory statistics course</em></u>

So, X ~ Binom(n = 20 , p = 0.20)

(a) Probability that 2 or fewer will withdraw is given by = P(X \leq 2)

P(X \leq 2) =  P(X = 0) + P(X = 1) + P(X = 2)

=  \binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}

=  1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}

=  <u>0.2061</u>

(b) Probability that exactly 4 will withdraw is given by = P(X = 4)

                      P(X = 4) =  \binom{20}{4} \times 0.20^{4} \times (1-0.20)^{20-4}

                                 =  4845\times 0.20^{4} \times 0.80^{16}

                                 =  <u>0.2182</u>

(c) Probability that more than 3 will withdraw is given by = P(X > 3)

P(X > 3) =  1 - P(X \leq 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

=  1-(\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}+\binom{20}{3} \times 0.20^{3} \times (1-0.20)^{20-3})

=  1-(1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}+1140\times 0.20^{3} \times 0.80^{17})

=  1 - 0.4114 = <u>0.5886</u>

(d) The expected number of withdrawals is given by;

                        E(X)  =  n\times p

                                 =  20 \times 0.20 = 4 withdrawals

You might be interested in
What is a scatter plot?<br> I somewhat know the answer, but I just need to know everything about it
EleoNora [17]
A scatter plot (also called scatterplot, scatter graph, scatter chart, or scatter diagram) is a type of plot or mathematical diagram using Cartesian coordinates to display values. For typically two variables for a set of data. Is the points are coded (color/shape/size), one additional variable can be displayed. The data are displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the verticals axis.
Hope that’s everything you wanted to know!
7 0
3 years ago
Find an equation of the circle that has a center (2,-4) and passes through (3,5).d
7nadin3 [17]

Answer:

um i think 3-5

Step-by-step explanation:

5 0
3 years ago
Find the radius of a circle with an area of 380 square inches. Round your answer to the nearest hundredth
KonstantinChe [14]

Answer:

Step-by-step explanation:

Area of a circle is defined as

A = πr²

Where

A is the area of the circle

r Is the radius of the circle

π is a constant = 3.142

Then,

Given that the area is 380 in²

So,

A = πr²

380 = 3.142 × r²

Divide both side by 3.142

380 / 3.142 = 3.142 × r² / 3.142

111.372 = r²

Take square root of both sides

√111.372 = √r²

10.5533 = r

r = 10.5533 in

Nearest hundredth means to 2d.p

Therefore

r = 10.55 inches

7 0
3 years ago
Read 2 more answers
Suppose Y varies directly with X and Y equals 10 when X equals -3 what direct variation equation relates XNY what is the value o
xeze [42]

Answer:

Expression: Y = -10/3 X

Y = 10/3

Step-by-step explanation:

If Y varies directly as X, then;

Y∝X

Y = kX

k is the constant of variation

If Y = 10 and X = -3

10 = -3k

k = -10/3

Substitute k = -10/3 into the expression Y = kX

Y = -10/3 X

This gives the required expression

To get the value of Y when X = -1

Recall that Y = kX

Y = -10/3 (-1)

Y = 10/3

Hence the value of Y is 10/3

8 0
3 years ago
The vertical change between 2 points
Levart [38]

Answer:

The vertical change between two points is called the rise, and the horizontal change is called the run.

6 0
2 years ago
Read 2 more answers
Other questions:
  • Set up an equation and solve for x<br> X<br> 2x<br> 3x<br> Equation
    9·1 answer
  • A goblet contains 2 red marbles, 6 green marbles, and 4 blue marbles.
    5·1 answer
  • PLEASE HELP ASAP NOW WILL MARK BRAINIEST LOTS OF POINTS!!!!
    11·1 answer
  • How are tax and discount the same?
    7·2 answers
  • Find the angle measurement of x.
    9·2 answers
  • Please help ASAP!! Please
    7·1 answer
  • 5/7x - 1/3x = 8<br> Plz help me due today
    13·2 answers
  • You run 6 miles in one hour and 24 miles in four hours.
    5·2 answers
  • Alexa wants to purchase some new supplies for making jewelry
    14·1 answer
  • Solve for the vaule of x:-<br> <img src="https://tex.z-dn.net/?f=2x%2B3%20%3D%205" id="TexFormula1" title="2x+3 = 5" alt="2x+3 =
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!