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Alex_Xolod [135]
3 years ago
7

A bookbook can be classified as either non dash fictionnon-fiction or fictionfiction. Suppose that 9494​% of booksbooks are clas

sified as fictionfiction. ​(a) Two booksbooks are chosen at random. What is the probability that both booksbooks are fictionfiction​? ​(b) FiveFive booksbooks are chosen at random. What is the probability that all fivefive booksbooks are fictionfiction​? ​(c) What is the probability that at least one of fivefive randomly selected booksbooks is non dash fictionnon-fiction​? Would it be unusual that at least one of fivefive randomly selected booksbooks is non dash fictionnon-fiction​?
Mathematics
1 answer:
DIA [1.3K]3 years ago
3 0

Answer:

a) 0.8836

b) 0.7339

c) 0.2342

Step-by-step explanation:

Books classified as fiction = 94% or 0.94 probability

Books classified as non-fiction = 1 - 0.94 = 0.06

a) for two books, we get: 0.94 * 0.94 = 0.8836 Probability

b) The probability that all five books are fiction is: 0.94^5

    This equals 0.7339 Probability

c) Probability that one books is non-fiction, while the other 4 are fiction is determined in the following way:

 Probability of non-fiction * probability of fiction^(number of books)

 0.06 * 0.94^4 = 0.0468

 This does not account for the order at which the non-fiction book shows up. Such as the non-fiction book being the first book picked, or in another case - the non-fiction book being the last picked.

Since there are 5 ways this could occur, the total probability will be calculated as shown: 0.0468 * 5 = 0.2342 Probability

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You have 2 boxes of 21 parts. On average, each individual work operation takes 3 minutes per part. At the end, packaging the ent
kenny6666 [7]

Answer:

2 hours, 26 minutes

Step-by-step explanation:

2 boxes of 21 parts = 42 total parts

3 minutes per part = 42 x 3 = 126 minutes

10 minutes per box to package = 10 x 2 = 20 minutes

126 + 20 = 146 minutes

2 hours = 120 minutes

146 - 120 = 26

Final Answer: 2 hours, 26 minutes

6 0
3 years ago
Please help me I don’t understand how to do it. If you can please use a data table to explain how to do it.
Ksivusya [100]

Answer:

The 70% mixture makes up 0.7 liters of the solution whereas the 60% mixture makes up 2.8 liters of the solution.

Step-by-step explanation:

Let us have x liters of the .7 mixture and y liters of the .6 mixture.

We want total liters to be 3.5 which means we need x+y=3.5 . I don't like the decimal in the equation so I'm going to multiply both sides by 10: 10x+10y=35

We also need the .7x+.6y=.62(3.5) . I hate the decimal business going on in this question so I'm going to multiply by 1000 which gives 700x+600y=62(35) .

So we have the system

700x+600y=62(35)

10x+10y=35

I'm going to setup this up for linear combination/elimination.

Multiply bottom equation by 60.

700x+600y=62(35)

600x+600y=60(35)

Subtract equations (bottom from top):

(700-600)x+(600-600)y=35(62-60)

Simplify:

100x+0y=35(2)

100x=70

Divide both sides by 100:

x=70/100

x=7/10

Going back to x+y=3.5 along with x=7/10 or .7 liters to find y.

y=3.5-x with x=.7

y=3.5-0.7

y=2.8

The 70% mixture makes up 0.7 liters of the solution whereas the 60% mixture makes up 2.8 liters of the solution.

Pic added.

Another way to do problem:

.7x+.6(3.5-x)=.62(3.5)

Multiply and distribute:

.7x+2.1-.6x=2.17

Combine like terms on left:

.1x+2.1=2.17

Subtract 2.1 on both sides:

.1x=.07

Multiply both sides by 10:

x=0.7 liters

Now the other acid solution is 3.5-0.7 which is 2.8 litera.

4 0
3 years ago
Four triangles are shown. One side of each triangle lies on a ray, and the triangles are not drawn to scale. Based on these tria
Firdavs [7]

Answer:

x=120 so the third one

Step-by-step explanation:

x=98+22

x=120

3 0
3 years ago
Read 2 more answers
Solve 2x2 + 5x = 12
aliya0001 [1]

2x2+5x=12, 2x+5x=7x, 12+2=14, 7x/7=14/7, x=2

4 0
3 years ago
Refer to the following scenario:You want to see if there is a difference between the exercise habits of Science majors and Math
bekas [8.4K]

Answer:

1. H0: P1 = P2

2. Ha: P1 ≠ P2

3. pooled proportion p = 0.542

4. P-value = 0.0171

5. The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

6. The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

Step-by-step explanation:

We should perform a hypothesis test on the difference of proportions.

As we want to test if there is significant difference, the hypothesis are:

Null hypothesis: there is no significant difference between the proportions (p1-p2 = 0).

Alternative hypothesis: there is significant difference between the proportions (p1-p2 ≠ 0).

The sample 1 (science), of size n1=135 has a proportion of p1=0.607.

p_1=X_1/n_1=82/135=0.607

The sample 2 (math), of size n2=92 has a proportion of p2=0.446.

p_2=X_2/n_2=41/92=0.446

The difference between proportions is (p1-p2)=0.162.

p_d=p_1-p_2=0.607-0.446=0.162

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{82+41}{135+92}=\dfrac{123}{227}=0.542

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.542*0.458}{135}+\dfrac{0.542*0.458}{92}}\\\\\\s_{p1-p2}=\sqrt{0.001839+0.002698}=\sqrt{0.004537}=0.067

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.162-0}{0.067}=\dfrac{0.162}{0.067}=2.4014

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

\text{P-value}=2\cdot P(z>2.4014)=0.0171

As the P-value (0.0171) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

We want to calculate the bounds of a 99% confidence interval of the difference between proportions.

For a 99% CI, the critical value for z is z=2.576.

The margin of error is:

MOE=z \cdot s_{p1-p2}=2.576\cdot 0.067=0.1735

Then, the lower and upper bounds of the confidence interval are:

LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.162-0.1735=-0.012\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.162+0.1735=0.335

The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

6 0
3 years ago
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