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3 years ago

Write an inequality for the graph below

Mathematics

1 answer:

Rufina [12.5K]3 years ago

4 0

Answer:

Y≥6

Step-by-step explanation:

Solid line means ___ or equal to, and since it goes from 6 down, it is less than, so less than or equal to.

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Consider the probability that greater than 26 out of 124 software users will call technical support. Assume the probability that

Mekhanik [1.2K]

Answer:

Since $n(1-p) = 3.72 < 10$ , the normal curve cannot be used as an approximation to the binomial probability.

100% probability that greater than 26 out of 124 software users will call technical support.

Step-by-step explanation:

Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

It is needed that:

$np \geq 10$ and $n(1-p) \geq 10$

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

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

And p is the probability of X happening.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

Out of 124 software users

This means that $n = 124$

Assume the probability that a given software user will call technical support is 97%.

This means that $p = 0.97$

Conditions:

$np = 124*0.97 = 120.28 \geq 10$

$n(1-p) = 124*0.03 = 3.72 < 10$

Since $n(1-p) = 3.72 < 10$ , the normal curve cannot be used as an approximation to the binomial probability.

Consider the probability that greater than 26 out of 124 software users will call technical support.

The lowest possible probability of those is 27, so, if it is 0, since it is considerably below the mean, 100% probability of being greater. We have that:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 27) = C_{124,27}.(0.97)^{27}.(0.03)^{97} = 0$

1 - 0 = 1

100% probability that greater than 26 out of 124 software users will call technical support.

3 0

3 years ago

What is the volume of the rectangular prism?<br><br> Type the answer in the boxes below.

Wittaler [7]

Answer:

15 cm^3

Step-by-step explanation:

I think it's 15 because if you count, there are 30 boxes. Each box has a volume of 1/2, so you are supposed to multiply, which means 1/2x30.

1/2x30=15

I hope it's right!

8 0

3 years ago

Mr. Altamirano opens an account with a simple interest on an account with $1000 at 3% annually for 9 months. How much interest d

gladu [14]

Answer:

1022.50

Step-by-step explanation:

1000*.03= 30. (12mos interest)

30/4=7.50 quarterly interest

7.50x3 (9mos)= 22.50 interest

7 0

3 years ago

What is the solution to the equation? <br><br> 14g=154

irinina [24]

Answer:

g = 11

Step-by-step explanation:

14g = 154

You have 14g. 14g means 14 times g. You want g alone. To get 14 alone, since g is being multiplied by 14, you must do the opposite operation. The opposite of multiplying by 14 is dividing by 14. The rule with equations is that you must do the same operation to both sides. Divide both sides by 14.

14g/14 = 154/14

g = 11

7 0

3 years ago

Read 2 more answers

A chef planning for a large banquet thinks that 2 out of every 5 dinner guests will order soup. 800 guests are going to be at th

Xelga [282]

Answer:

The Chef will prepare 320 soups for a large banquet

Step-by-step explanation:

chef thinks that 2 out of every 5 dinner guests will order soup

===> Order soup / total number of attender

= 2/5

Total guest = 800 ==> 4 people ordered soup is

2 /5 = x /800

cross multiplying

x = 2 x 800 / 5

= 320

The Chef will prepare 320 soups for a large banquet

8 0

4 years ago