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oksano4ka [1.4K]
3 years ago
7

There are 8 girls for every 7 boys on a field trip.if there 56 girls on the trip how many students are on the trip

Mathematics
1 answer:
Ket [755]3 years ago
8 0

Well the first thing you need to do is set up a proportion.

8 girls         56 girls                          

--------    =   -----------

7 boys             x


Now what we have to do is find out what we multiplied by 8 to get 56.

Simply divide.

56 ÷ 8 = 7

So, we figured out that the magic number is 7!

So we multiply the boy number by 7

7 x 7 = 49

So this means that there are 49 boys on the field trip.

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2.618-2.98\frac{0.078}{\sqrt{15}}=2.56    

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So on this case the 99% confidence interval would be given by (2.56;2.68)

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".

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the mean and the sample deviation we can use the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n} (2)  

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}} (3)  

The mean calculated for this case is \bar X=2.618

The sample deviation calculated s=0.078

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=15-1=14

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,14)".And we see that t_{\alpha/2}=2.98

Now we have everything in order to replace into formula (1):

2.618-2.98\frac{0.078}{\sqrt{15}}=2.56    

2.618+2.98\frac{0.078}{\sqrt{15}}=2.68    

So on this case the 99% confidence interval would be given by (2.56;2.68)    

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