How many different ways can 3 events be ordered?

Mathematics

2 answers:

Gnoma [55]3 years ago

7 0

Step-by-step explanation:

I kind of forgot but it should be 6

3!=6

for the first event there are three choices, then 2, then 1. You them multiply them all.

Im sorry if this made no sense lol, i will delete if people in the comments want to give a better explanation.

beks73 [17]3 years ago

6 0

Answer:

Step-by-step explanation:

Label them as variables

A, B, and C

Now try and list them

ABC

ACB

BAC

BCA

CAB

CBA

There should be 6

The more mathematical way is using factorials

So you would do 3! which is 3*2*1

This also gives you 6

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The Ohio Department of Agriculture tested 203 fuel samples across the state

Rus_ich [418]

Answer:

$\hat p = \frac{14}{105}= 0.133$

And that represent the proportion of failures.

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.133 - 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.0475$

$0.133 + 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.2185$

The 99% confidence interval would be given by (0.0475;0.2185)

Step-by-step explanation:

Previous concept

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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 population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by: