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Akimi4 [234]
3 years ago
9

Sharon has collected donations of $4.40, $3.12, $8.00, and $6.22 to help buy books for the new library. What is the mean (averag

e) amount of donations she has collected?
Mathematics
1 answer:
jekas [21]3 years ago
3 0

Answer:5.435

Step-by-step explanation: In math, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. To find this answer, we need to find the average of a set of data, we add up all the values and divide this total by the numbers of values. So if you add 4.40, 3.12, 8.00 and 6.22 together, we get 21.74. There are four values (4.40, 3.12, 8.00 and 6.22) so we divide the amount of values there are, which would be four. 21.47/4 would then get you 5.435

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5 0
3 years ago
The following data were collected from 12 rain gauges in a park. Build a 95% CI for the mean rainfall at the park.
dybincka [34]

Answer:

Critical values:t_{\alpha/2}=-2.201 t_{1-\alpha/2}=2.201

95% confidence interval would be given by (3.646;4.472)

Step-by-step explanation:

1) 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 data is:

4.65 3.89 2.73 4.35 3.80 4.86 4.33 4.37 4.76 4.05 3.05 3.87

2) Compute the sample mean and sample standard deviation.

In order to calculate the mean and the sample deviation we need to have on mind the following formulas:  

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

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

=AVERAGE(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

On this case the average is \bar X= 4.059

=STDEV.S(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

The sample standard deviation obtained was s=0.6503

3) Find the critical value t* Use the formula for a CI to find upper and lower endpoints

In order to find the critical value we need to take in count that our sample size n =12 <30 and on this case we don't know about the population standard deviation, so on this case we need to use the t 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. The degrees of freedom are given by:

df=n-1=12-1=11

We can find the critical values in excel using the following formulas:

"=T.INV(0.025,11)" for t_{\alpha/2}=-2.201

"=T.INV(1-0.025,11)" for t_{1-\alpha/2}=2.201

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

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

And we can use Excel to calculate the limits for the interval

Lower interval : "=4.059 -2.201*(0.6503/SQRT(12))" =3.646

Upper interval :  "=4.059 +2.201*(0.6503/SQRT(12))" =4.472

So the 95% confidence interval would be given by (3.646;4.472)

8 0
3 years ago
The nth term of the sequence is n^2 + 20 <br> How many terms in the sequence are less than 50
Alex Ar [27]

Answer:

5 terms

Step-by-step explanation:

nth term of the sequence =n^2 + 20

an= n^2 + 20

1st term when n= 1

1^2 + 20= 20

2nd term n= 2

2^2 + 20=24

3rd term when n= 3

3^2 + 20= 29

4th term when n= 4

4^2 + 20= 36

5th term when n= 5

5^2 + 20 =45

6th term when n= 6

6^2 + 20=56

Hence, terms in the sequence are less than 50 are first 5 terms

6 0
3 years ago
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