Which number is NOT in the solution set of the inequality x

The rocks are chosen without replacement, which means that the hypergeometric distribution is used to solve this question. First we get the parameters, and then we answer the questions. From this, we get that:

$E(X) = 5.25, Var(X) = 0.5966$
P(X < 6) = 0.9545
P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The mean and the variance are:

$\mu = \frac{nk}{N}$

$\sigma^2 = \frac{nk(N-k)(N-n)}{N^2(N-1)}$

We have that:

5 + 7 = 12 rocks, which means that $N = 12$

9 are chosen, which means that $n = 9$

7 are granite, which means that $k = 7$

Question a:

$E(X) = \mu = \frac{9\times7}{12} = 5.25$

$Var(X) = \sigma^2 = \frac{9\times7(12-7)(12-9)}{12^2(12-1)} = 0.5966$

Thus:

$E(X) = 5.25, Var(X) = 0.5966$

Question b:

Since there are only 5 specimens of basaltic rock, at least 9 - 5 = 4 specimens of granite are needed, which means that:

$P(X < 6) = P(X = 4) + P(X = 5) + P(X = 6)$

In which

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 4) = h(4,12,9,7) = \frac{C_{7,4}*C_{5,5}}{C_{12,9}} = 0.1591$

$P(X = 5) = h(5,12,9,7) = \frac{C_{7,5}*C_{5,4}}{C_{12,9}} = 0.4773$

$P(X = 6) = h(6,12,9,7) = \frac{C_{7,6}*C_{5,3}}{C_{12,9}} = 0.3181$

Thus

$P(X < 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.1591 + 0.4773 + 0.3181 = 0.9545$

So P(X < 6) = 0.9545.

Question c:

5 of basaltic and 4 of granite: 0.1591 probability.

7 of granite is P(X = 7), in which

$P(X = 7) = h(7,12,9,7) = \frac{C_{7,7}*C_{5,2}}{C_{12,9}} = 0.0455$

0.1591 + 0.0455 = 0.2046, thus:

P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.

A similar question is found at brainly.com/question/24008577

5 0

3 years ago

here you go:) [(-2/3, 7/2]. 3x-8y = 1. * 16x+2y=1114. + 24x+8y=44. 27y=45. (2x-5y=-472. 4x+3y=5. - 4x70y=8. 13y=13. 27 27. (5x-2

deff fn [24]

Answer:

Step-by-step explanation:

BRO I DONT KNOW HELP CRI

8 0

2 years ago

helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. she also needs 0.75 cup of sugar pe

tatuchka [14]

The <em><u>correct answer</u></em> is:

She can make 2 loaves of bread and 4 batches of muffins.

Explanation:

Let b represent bread and m represent muffins.

The equation for the amount of flour she needs is 3.5b+2.5m=17.

The equation for the amount of sugar she needs is 0.75b+0.75m=4.5.

To solve this, we will want to eliminate one of the variables. To do this, we will make the coefficients of one of the variables the same. If we multiply 2.5 by 0.3, we get 0.75; this is what we will do to the first equation:

$\left \{ {{0.3(3.5b+2.5m=17)} \atop {0.75b+0.75m=4.5}} \right. \\ \\\left \{ {{1.05b+0.75m=17} \atop {-(0.75b+0.75m=4.5)}} \right. \\ \\0.3b=0.6 \\ \\\frac{0.3b}{0.3}=\frac{0.6}{0.3} \\ \\b=2$

She can bake two loaves of bread.

Substituting 2 for b in the first equation, we have

3.5(2)+2.5m=17

7+2.5m=17

Subtract 7 from each side:

7+2.5m-7=17-7

2.5m=10

Divide both sides by 2.5:

2.5m/2.5 = 10/2.5

m = 4

She can bake 4 batches of muffins.

6 0

3 years ago

Read 2 more answers

Which number is NOT in the solution set of the inequality x > 10?