SO,

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

julsineya [31]

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.

5 0

3 years ago

What is the length x of the right triangle, rounded to the nearest<br> tenth?

Zarrin [17]

Answer:

109.5; B

Step-by-step explanation:

From your identity,

CosA = adjacent/ hypothenus

A represent an arbitrary angle between the sides in question.

In the question above, A=64

Hypothenus is the longest side and adjacent is the side just below the angle .

In the above case,

Hypothenus= X

adjacent =48

This means;

Cos64 = 48 /X

X = 48 / cos64; [ from cross multiplication and diving through by cos64]

X = 48 /0.4383 [ cos64 in radian = 0.4383]

= 109.51

= 109.5 to the nearest tenth.

Note( do your calculation of angle in radian or else, you won't get the answer)

6 0

2 years ago

A consumer affairs investigator records the repair cost for 4 randomly selected washers. A sample mean of $64.26 and standard de

Mashutka [201]

Answer:

Critical value: z = 1.28

The 80% confidence interval for the mean repair cost for the washers is between $46.487 and $82.033.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.80}{2} = 0.10$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$

So it is z with a pvalue of 1-0.1 = 0.9, so z = 1.28

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

So

$M = 1.28*\frac{27.77}{\sqrt{4}} = 17.773$

The lower end of the interval is the mean subtracted by M. So 64.26 - 17.773 = $46.487.

The upper end of the interval is M added to the mean. So 64.26 + 17.773 = $82.033.

The 80% confidence interval for the mean repair cost for the washers is between $46.487 and $82.033.

7 0

3 years ago

If a 15 ft tall adult giraffe casts a 18 ft long shadow, then how long is the shadow that a 5 ft tall bird bath casts?

Lemur [1.5K]

Answer:

<h3>x = 6 ft. long shadow</h3><h3></h3>

Step-by-step explanation:

its a ratio and proportion:

<u> 15 ft. tall giraffe </u> = <u> 5 ft. tall bird </u>

18 ft. shadow x shadow

15 (x) = 18 (5)

x = 90 / 15

x = 6 ft. long shadow

8 0

3 years ago

Eight f subtract three f plus two plus five equals

Zolol [24]

Answer:

5f + 7

Step-by-step explanation:

8f-3f+2+5

8f-3f is 5f and 2 + 5 is 7

5f+7

6 0

3 years ago

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