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
solmaris [256]
3 years ago
15

A construction company is considering submitting bids for contracts of three different projects. The company estimates that it h

as a 10% chance of winning a given bid and that winning bids are independent of one another. Let X-the number of bids won by the company.
a. Write out the PMF of X.
b. How many bids can the company expect to win?
c. What is the standard deviation of the number of bids won?
It costs the company $10,000 to prepare and submit all three bids. If the company wins the bid, it will produce S50,000 of income to the company. What is the expected profit for the company?
Mathematics
1 answer:
julsineya [31]3 years ago
5 0

Answer:

a.P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\

b. E(x) = 0.3

c. S(x)=0.5196

d. E=5,000

Step-by-step explanation:

The probability that the company won x bids follows a binomial distribution because we have n identical and independent experiments with a probability p of success and (1-p) of fail.

So, the PMF of X is equal to:

P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\

Where p is 0.1 and it is the chance of winning. Additionally, n is 3 and it is the number of bids. So the PMF of X is:

P(x)=\frac{3!}{x!(3-x)!}*0.1^{x}*(1-0.1)^{n-x}\\

For binomial distribution:

E(x)=np\\S(x)=\sqrt{np(1-p)}

Therefore, the company can expect to win 0.3 bids and it is calculated as:

E(x) = np = 3*0.1 = 0.3

Additionally, the standard deviation of the number of bids won is:

S(x)=\sqrt{np(1-p)}=\sqrt{3(0.1)(1-0.1)}=0.5196

Finally, the probability to won 1, 2 or 3 bids is equal to:

P(1)=\frac{3!}{1!(3-1)!}*0.1^{1}*(1-0.1)^{3-1}=0.243\\P(2)=\frac{3!}{2!(3-2)!}*0.1^{2}*(1-0.1)^{3-2}=0.027\\P(3)=\frac{3!}{3!(3-3)!}*0.1^{3}*(1-0.1)^{3-3}=0.001

So, the expected profit for the company is equal to:

E=-10,000+50,000(0.243)+100,000(0.027)+150,000(0.001)\\E=5,000

Because there is a probability of 0.243 to win one bid and it will produce 50,000 of income, there is a probability of 0.027 to win 2 bids and it will produce 100,000 of income and there is a probability of 0.001 to win 3 bids and it will produce 150,000 of income.

You might be interested in
Sam has purchased a $30,000 car for his business. The car depreciates 30% every year. What is the explicit formula for this sequ
Step2247 [10]
If your just figuring out how much the car depreciated just by driving off the lot new...1st year.
$30,000×.30=$9,000

$30,000- $9,000=$21,000.

just take the brand new value of the car multiplied by the .30% of the 1st depreciation...take that answer ($9,000) and subtract it from your orginal value of $31,000.

which gives you $21,000

8 0
3 years ago
Read 2 more answers
Find the following sets
Irina-Kira [14]

Answer:

Step-by-step explanation:

a) 2,3,4,5,6,7

b)4,6,7

5 0
2 years ago
Bryan sells cars. He makes a salary of $500 a week, plus $150 for every car he sells. This week, he wants to make at least $2000
Kobotan [32]
If Bryan wants to make $2000 dollars then he needs to solve this equation:

2000=500+150x
-500   -500

1500=150x   divide by 150 on both sides

x=10

10 cars
  
3 0
3 years ago
Read 2 more answers
What is the mass of an object that has a volume of 34 cm^4 and a densityof 6 g/cm^3?
lakkis [162]

Answer:

Mass = density * volume

Mass = 6 g/cm^3 / 34 cm^3

Mass = 0.1764705882 grams

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
10 points
dsp73

Answer:

A

Step-by-step explanation:

I hope this helps and sorry if I'm wrong!

4 0
2 years ago
Other questions:
  • Simplify <br><br> √250x^16 / √2x
    8·1 answer
  • Solve the following System of Three Equations: x−3y+z=−15<br> 2x+y−z=−2<br> x+y+2z=1
    5·1 answer
  • 3+(-7)<br> What is the answer
    13·2 answers
  • A group of eight friends (five girls and three boys) plans to watch a movie but they have only five tickets how many different c
    11·1 answer
  • VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV this is middle school math
    13·1 answer
  • I Only Need #9 Not 10
    15·1 answer
  • Which of the following fractions is larger in these fractions 1 1/4, 1/6, 1 1/24?
    7·1 answer
  • Please help this is due soon, whoever answers correctly will get a brainy!
    5·2 answers
  • School started at 9:15am. After two period lasting 50min each, children had a break. At what time was the break?
    10·2 answers
  • I don't know how to delete a question how can I do that?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!