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ira [324]
4 years ago
8

A philanthropic organisation sent free mailing labels and greeting cards to a random sample of 100 comma 000100,000 potential do

nors on their mailing list and received 47034703 donations. ​(a) Give a 9999​% confidence interval for the true proportion of those from their entire mailing list who may donate. ​(b) A staff member thinks that the true rate is 4.74.7​%. Given the confidence interval you​ found, do you find that rate​ plausible?
Mathematics
1 answer:
nata0808 [166]4 years ago
3 0

Answer:

a) 99% Confidence interval:  (0.045311,0.04875)

b) 4.7% is a plausible rate.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 100,000

Number of people who donated, x = 4703

\hat{p} = \dfrac{x}{n} = \dfrac{4703}{100000} = 0.04703

a) 99% Confidence interval:

\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

z_{critical}\text{ at}~\alpha_{0.01} = 2.58

Putting the values, we get:

0.04703\pm 2.58(\sqrt{\dfrac{0.04703(1-0.04703)}{100000}})\\\\= 0.04703\pm 0.00172\\\\=(0.04531,0.04875)

b) A staff member thinks that the true rate is 4.74.7​%.

Yes, this is a plausible rate as this value of 0.0474 lies in the calculated confidence interval as:

4.531\%

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What is the outlier in the following data set:<br> 15,11,10,8,9,1,8,7,5,4,2,3, and 37?
NeTakaya

Step-by-step explanation:

The steps to find an outlier:

1. Put the data in numerical order.

2. Find the median.

3. Find the medians for the top and bottom parts of the data. This divides the data into 4 equal parts.

The median with the smallest value is called Q1. The median for all the values - usually just called the median is also called Q2. The median with the largest value is Q3.

4. Subtract...Q3 - Q1. This value is the InterQuartileRange or IQR. Remember that the range means taking the largest minus the smallest. This is a special range having to do with the quartiles.

5. Multiply...1.5 * IQR

6. Take your answer from #5 and do 2 things with it. A). Subtract it from Q1 and B) Additional to Q3.

7. Look at all your data points. If any are SMALLER than Q1 - 1.5 *IQR, they are outliers. If any are LARGER than Q3 + 1.5 *IQR, they are also outliers.

For your data....the median, Q2 is

(43+38)/2 = 40.5.

Q1 = (30+26)/2 = 28.

Q3 = (54+52)/2 = 53

The IQR is 53 - 28 = 25

1.5 * IQR = 37.5

Q1 - 37.5 = 28 - 37.5 = -9.5. There is no data value less than -9.5.

Q3 + 37.5 = 53 + 37.5 = 90.5. there is no data value greater than 90.5.

My conclusion is that there are no outliers in this data.

I hope this helps!

4 0
3 years ago
Will give the brainliest answer,
IrinaK [193]
The answer to this would be $30.67

First of all APR is the wrong term for interest earned on a deposit. So I'm going to guess that you really mean simple interest. Step one figure the amount in the emergency fund. Since the monthly expenses are $1,157.65, you multiply 4 months times $1,157.65: 4($1,157.65) = $4,606.60

Step 2, figure out how much is 25% of $4,606.60. So change the percent in a decimal by moving the decimal to the left two places. So 25.0 becomes .25. Or you could divide 25 by 100 and get .25 Next multiply .25 times $4,606.60 and you get $1,151.65 for the amount in the savings account.

Step 3, subtract the amount in deposited in the savings account from the total amount in the emergency fund. So you $4,606.60 minus $1,151.65 Which gets you $3,454.95 in the CD.

Step 4, Calculate the interest earned in the savings account. Since the savings account earns 3.3% a year and there are 365 days in a non leap year, divide 3.3% by 365 to find out how much interest is earned a day and multiply it times the amount in the savings account. First change 3.3% to a decimal by moving the decimal point to the left two places. Which gets us .033 So .033 divided by 365 times $1,151.65 Which gets us about $0.104 in interest a day. Finally, multiply the interest earned each day by 60 days. $0.104 times 60 Which gets us about $6.25 in interest earned on the savings account for 60 days.

Step 5, Find the interest earned on the CD. Since the CD earns 4.3% interest a year and there are 365 days in a non leap year, divide 4.3% by 365 to find out how much interest is earned a day and multiply it times the amount in the CD. First change 4.3% to a decimal by moving the decimal point to the left two places. Which gets us .043. So .043 divided by 365 times $3,454.95 Which gets us about $0.407 in interest a day. Finally, multiply the interest earned each day by 60 days. $0.407 times 60. Which gets us about $24.42 in interest earned on the CD for 60 days

Step 6, The total interest earned on the savings account and the CD is: $24.42 + 6.25 = $30.67






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