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
natta225 [31]
3 years ago
12

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

istered for the course. a. Compute the probability that or fewer will withdraw (to 4 decimals). b. Compute the probability that exactly will withdraw (to 4 decimals). c. Compute the probability that more than will withdraw (to 4 decimals). d. Compute the expected number of withdrawals.
Mathematics
1 answer:
polet [3.4K]3 years ago
5 0

Answer:

A university found that 30% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.

a. Compute the probability that 2 or fewer will withdraw (to 4 decimals).

= 0.0355

b. Compute the probability that exactly 4 will withdraw (to 4 decimals).

= 0.1304

c. Compute the probability that more than 3 will withdraw (to 4 decimals).

= 0.8929

d. Compute the expected number of withdrawals.

= 6

Step-by-step explanation:

This is a binomial problem and the formula for binomial is:

P(X = x) = nCx p^{x} q^{n - x}

a) Compute the probability that 2 or fewer will withdraw

First we need to determine, given 2 students from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by:

P(X = x) = nCx p^{x} q^{n - x}\\P(X = 2) = 20C2(0.3)^2(0.7)^{18}\\P(X = 2) =190 * 0.09 * 0.001628413597\\P(X = 2) = 0.027845872524

P(X = x) = nCx p^{x} q^{n - x}\\P(X = 1) = 20C1(0.3)^1(0.7)^{19}\\P(X = 1) =20 * 0.3 * 0.001139889518\\P(X = 1) = 0.006839337111

P(X = x) = nCx p^{x} q^{n - x}\\P(X = 0) = 20C0(0.3)^0(0.7)^{20}\\P(X = 0) =1 * 1 * 0.000797922662\\P(X = 0) = 0.000797922662

Finally, the probability that 2 or fewer students will withdraw is

P(X = 2) + P(X = 1) + P(X = 0) \\= 0.027845872524 + 0.006839337111 + 0.000797922662\\= 0.035483132297\\= 0.0355

b) Compute the probability that exactly 4 will withdraw.

P(X = x) = nCx p^{x} q^{n - x}\\P(X = 4) = 20C4(0.3)^4(0.7)^{16}\\P(X = 4) = 4845 * 0.0081 * 0.003323293056\\P(X = 4) = 0.130420974373\\P(X = 4) = 0.1304

c) Compute the probability that more than 3 will withdraw

First we will compute the probability that exactly 3 students withdraw, which is given by

P(X = x) = nCx p^{x} q^{n - x}\\P(X = 3) = 20C3(0.3)^3(0.7)^{17}\\P(X = 3) = 1140 * 0.027 * 0.002326305139\\P(X = 3) = 0.071603672205\\P(X = 3) = 0.0716

Then, using a) we have that the probability that 3 or fewer students withdraw is 0.0355+0.0716=0.1071. Therefore the probability that more than 3 will withdraw is 1 - 0.1071=0.8929

d) Compute the expected number of withdrawals.

E(X) = 3/10 * 20 = 6

Expected number of withdrawals is the 30% of 20 which is 6.

You might be interested in
A tennis ball machine can launch 60 tennis balls in 12 minutes. At this rate,how many tennis balls can it launch in 2 hours?
Lapatulllka [165]
12*5=60
12*10=120
60*10=600
The answer is 600
7 0
3 years ago
Awarding brainliest!!!
Alex Ar [27]

Answer:

m=3

Step-by-step explanation:

6m+5-3m=7(m-1)

Combine like terms

3m+5=7(m-1)

Distribute the 7

3m+5=7m-7

Subtract 3m from each side

4m-7=5

Add 7 to each side

4m=12

Divide by 4

m=3

8 0
3 years ago
Read 2 more answers
Can you factor 25m^2-10mn+n^2
Charra [1.4K]
You can factor it into (-5m+n)(-5m+n)
4 0
3 years ago
Jerry paid $54.40 for 4 Circus tickets. Each ticket cost the same amount. What was the cost of each Circus ticket in dollars and
AnnyKZ [126]

Answer : 13.6

Each ticket

4 0
2 years ago
Read 2 more answers
The Art and History Museum offers a family discount card for a donation of $57. I The table shows the price per person with and
Murljashka [212]

Answer:

8 number of visits will be the total cost of the visits (including the price of the discount card) be less expensive for a family of 2 adults and 1 child if they have purchased the discount card

Step-by-step explanation:

                             Price without Discount Card   Price with Discount Card

Ticket (12 & Under)        $10                                             $8

Adult's Ticket                  $15                                           $12

Let x be the number of visits

Price without discount card for 2 adults and 1 child ticket

Price without discount for x visits = x(15 \times 2+ 10)=40x

Price with discount for x visits =57+ x(12 \times 2+ 8)=57+32x

Now to find For what number of visits will the total cost of the visits (including the price of the discount card) be less expensive for a family of 2 adults and 1 child if they have purchased the discount card

57+32x< 40x

57<8x

7.1<x

So, 8 number of visits will be the total cost of the visits (including the price of the discount card) be less expensive for a family of 2 adults and 1 child if they have purchased the discount card

8 0
3 years ago
Other questions:
  • An acute triangle has side lengths 21 cm, X cm, and 2x cm. If 21 is one of the shorter side of the triangle, what is the greates
    11·2 answers
  • If 5 pieces of chocolate =27g how many pieces are there in 390g
    11·1 answer
  • *click image*
    11·1 answer
  • Y+5=_7x – 4)<br> -<br> Help !!
    10·2 answers
  • A. Cual De Las Siguientes Medidas No Se Debería Escribir En Notación Científica:
    9·1 answer
  • Please helpp. I have to get this done before 10:05.
    5·1 answer
  • Could you help me solve this? Three of the expression filled in the y sections only. And whether each equation is even or odd.
    13·1 answer
  • 3(x + 4) − x &gt; 4 <br> lol i dont know the answer
    15·1 answer
  • 2x+3y=15<br> X+y=6<br> Simultaneously equations
    14·2 answers
  • WILL GIVE BRAINLIEST
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!