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kvasek [131]
3 years ago
13

There are 25 students. Four of these students are selected to attend four different conferences. The first student selected will

go to
a conference in Makati city, the second will go to Paranaque city, the third to Quezon city and the fourth to Caloocan city. How

many such selections are possible?

256

12,650

303,600

390,625
Mathematics
1 answer:
irina1246 [14]3 years ago
7 0

Answer:

the number of possible selection is 12650

Option b) 12650  is the correct answer.

Step-by-step explanation:

Given the data in the question;

total number of students n = 25

number of student selected r = 4

^nC_r = ²⁵C₄

= 25! / ( 4!( 25 - 4 )! )

= 25! / (4!(21)!)

=  12650

Therefore, the number of possible selection is 12650

Option b) 12650  is the correct answer.

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3. Using the sample size of 800 and the proportion 0.47, calculate the margin of error associated with the estimate of the propo
salantis [7]

Answer:

ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346  

Step-by-step explanation:

Previous concepts

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

We assume for this case a confidence level of 95%. 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 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

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}}

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And if we replace the values obtained we got this:

ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346  

6 0
2 years ago
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