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Gelneren [198K]
3 years ago
12

Use properties to find the sum or product of 93+(68+7)

Mathematics
1 answer:
zaharov [31]3 years ago
7 0
93 + (68 + 7)
93 + 75
168
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What is the probability that a randomly selected member of a normally distributed population will lie more than 1.8 standard dev
Helen [10]

Answer:

P(X> \mu +1.8\sigma)=P(\frac{X-\mu}{\sigma}>\frac{\mu +1.8\sigma-\mu}{\sigma})=P(Z>1.8)

And we can find this probability using the complement rule:

P(z>1.8)=1-P(z

And using the normal standard distirbution table or excel we got:

P(z>1.8)=1-P(z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the variable if interest of a population, and for this case we know the distribution for X is given by:

X \sim N(\mu,\sigma)  

We are interested on this probability

P(X>\mu +1.8 \sigma)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X> \mu +1.8\sigma)=P(\frac{X-\mu}{\sigma}>\frac{\mu +1.8\sigma-\mu}{\sigma})=P(Z>1.8)

And we can find this probability using the complement rule:

P(z>1.8)=1-P(z

And using the normal standard distirbution table or excel we got:

P(z>1.8)=1-P(z

5 0
3 years ago
6m+2÷8=37 what does m=
Mama L [17]
6m+2/=37×8
6m=296-2
6m=294
m=49
4 0
3 years ago
Read 2 more answers
If F(x) = 4%-3, which of the following is the inverse of F(x)?
Brums [2.3K]

I assume you meant to type x for %.

If not, basically back-substitute at the end of the solution.

F(x) = 4x - 3

Let y = F(x)

y = 4x - 3

x = 4y - 3

x - 3 = 4y

(x - 3)/4 = y

Let y = F^(-1)x

F^(-1)x = (x - 3)/4

If you want % in your answer, just replace x for % in your answer.

8 0
3 years ago
Which statement best describes the meaning of the term average waiting-<br> time?
kotegsom [21]

Answer:

The average number of trials required to get the first success

5 0
3 years ago
It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken if the desir
Ksju [112]

Answer:

We need a sample size of at least 75.

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{1-0.95}{2} = 0.025

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 1-0.025 = 0.975, so z = 1.96

Now, we 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.

The standard deviation is the square root of the variance. So:

\sigma = \sqrt{484} = 22

With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is

We need a sample size of at least n, in which n is found when M = 5. So

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

5 = 1.96*\frac{22}{\sqrt{n}}

5\sqrt{n} = 43.12

\sqrt{n} = \frac{43.12}{5}

\sqrt{n} = 8.624

(\sqrt{n})^{2} = (8.624)^{2}

n = 74.4

We need a sample size of at least 75.

6 0
3 years ago
Read 2 more answers
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