Help help help pleaseeeee question down below

Geologist has collected 10 specimens of basaltic rock and 10th specimens of granite. The geologist instructs a laboratory assist

olya-2409 [2.1K]

Answer:

$p(5)=0.00136$

(a) $p(x)=\frac{(10Cx)*((10)C(15-x))}{20C10}$

(b) $p(10)+p(5)=0.00272$

(c) $p(7)+p(8)=0.0584$

Step-by-step explanation:

If we have N elements with k elements that we consider success and N-k elements that we consider fail, and we take a sample of n elements, the probability that there are x successes in the sample follows a hypergeometric distribution, so it is calculated as:

$p(x)=\frac{(kCx)*((N-k)C(n-x))}{NCn}$

In this case, N is equal to 20, k is equal to 10 specimens of granite rock, N-k is equal to 10 specimens of basaltic rock and n is 15. So, the probability that there are x specimens of granite rock in the sample or the pmf of the number of granite specimens selected for analysis is:

$p(x)=\frac{(10Cx)*((10)C(15-x))}{20C10}$

Now, the probability of getting exactly 5 granite specimens selected for analysis is:

$p(5)=\frac{(10C5)*((10)C(15-5))}{20C10}=0.00136$

On the other hand, the probability that all specimens of one of the two types of rock are selected for analysis is the probability to select 10 granite specimens or 10 basaltic specimens. Where the probability to take 10 basaltic specimens is equal to the probability to take 5 granite specimens.

Then, the probability that all specimens of one of the two types of rock are selected for analysis is:

$p(10)+p(5)=\frac{(10C10)*((10)C(15-10))}{20C10}+\frac{(10C5)*((10)C(15-5))}{20C10}\\p(10)+p(5)=0.00136+0.00136=0.00272$

For the hypergeometric distribution, the mean E(x) and standard deviation S(x) are:

$E(x)=\frac{nk}{N}=\frac{15*10}{20}=7.5\\S(x)=\sqrt{\frac{nk}{N}*(1-\frac{k}{N})*(\frac{N-n}{N-1})}\\S(x)=\sqrt{\frac{15*10}{20}*(1-\frac{10}{20})*(\frac{20-15}{20-1})}=0.9934$

Then, the number of granite specimens within 1 standard deviation of its mean value is:

E(x) - S(x) ≤ mean ≤ E(x) + S(x)

7.5-0.9934 ≤ mean ≤ 7.5+0.9934

6.5066 ≤ mean ≤ 8.4934

7 ≤ mean ≤ 8

Finally, the probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value is:

$p(7)+p(8)=\frac{(10C7)*((10)C(15-7))}{20C10}+\frac{(10C8)*((10)C(15-8))}{20C10}\\p(10)+p(5)=0.0292+0.0292=0.0584$

8 0

4 years ago

a students pay of $23 an hour at a new job is $6 more than twice the amount of the student earned per hour at an internship . wr

DanielleElmas [232]

23=(x*2)+6.
17=x*2
x=8 dollars an hour

4 0

3 years ago

How many 0.35 L glasses can you fill with a 1.65 L bottle of water

ycow [4]

Answer:

<h3>4.71 glasses </h3>

Steps:

Let say you can fill N no of 0.35 L glasses with 1.65 L.

Then,

N times 0.35 =1.65

N × 0.35=1.65

N=1.65/0.35

N=4.71

It means you can fill 4 glasses completely and 71% of the 5th glass.

7 0

4 years ago

What is the surface area of the solid

ozzi

What is the surface area of the solid?

The sum of the area of all of the faces or surface that enclose the solid.

7 0

2 years ago

Read 2 more answers

If someone could please help me, I want to make sure that the steps are correct.

Leya [2.2K]

Your answer would be the last option, c = √(E/m).

We can see this when we rearrange the equation, as:

E = mc²
÷ m
E/m = c²
√
√(E/m) = c

So you got all the steps in rearranging correct :)

I hope this helps!

7 0

3 years ago