The table shows a direct variation.

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

polet [3.4K]

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.

5 0

3 years ago

PLEASE ANSWER I WILL GIVE 30 POINTS!

Bingel [31]

Answer:

So the correct answer is"none of the above".

Step-by-step explanation:

z+(z+6)=z+z+6=2z+6. \\ \\ (z+z)+(z+6)=z+z+z+6=3z+6. \\ \\ (z+6)+6=z+12 \\ \\

4 0

3 years ago

−5.2 + y = 7.5

klio [65]

Answer:

your answer is

d. y = 12.7

5 0

3 years ago

Read 2 more answers

-1/5y+7=7<br> What is the value of y?

liq [111]

The answer is y=0

See the attached photo for details

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

8 0

2 years ago

A) NO CHANGE<br> B) City in the 1860s,<br> C) City, in the 1860s,<br> D) City in the 1860s

Oliga [24]

The correct option is B. City in the 1860s.

Conference In Two Years is the full form of CITY, CITY stands for Conference In Two Years, or Conference In Two Years is the complete name of the given abbreviation.

Any person whose salary is payable, in whole or in part, from the City treasury is referred to as a "City Official," as is any employee, officer, or elected official of the City.

Life as it is lived in a city, especially when compared to that of a small town, hamlet, etc.; the way of life thought to be typical of city dwellers.

Disclaimer

City in the 1860s- stole more than $30 millions.

Choose the correct option

A) NO CHANGE

B) City in the 1860s,

C) City, in the 1860s,

D) City in the 1860s

Learn more about City here

brainly.com/question/237028

#SPJ4

4 0

1 year ago