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N76 [4]
3 years ago
13

you purchased 10.75 gallons of gasoline at 3.60/gallon. you also bought a cookie (1.25) and windshield wiper fluid at (4.97). th

e state had a food tax of 4%. you gave the clerk 20.00 and the remaining amount is owed was charged to your debit card. how much was charged to your debit card
Mathematics
1 answer:
elixir [45]3 years ago
6 0
Here is the solution of the given problem above:
Given: Gasoline = 10.75 gallons x $3.60 = $38.70
           Cookie = $1.25 + food tax 4% = $1.30
           Wiper fluid = $4.97
           Cash = $20.00
           ? = amount charged on debit card
In order to know how much was charged, we first need to add all the other expenses.  So the total would be $44.97. Deduct $20 from it so the amount charged to the debit card is $24.97. Hope this answer helps.
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An SRS of 350 high school seniors gained an average of x¯=21 points in their second attempt at the SAT Mathematics exam. Assume
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Answer:

a) 21-2.58\frac{52}{\sqrt{350}}=13.83  

21+2.58\frac{52}{\sqrt{350}}=28.17  

So on this case the 99% confidence interval would be given by (13.83;28.17)  

b) ME=2.58\frac{52}{\sqrt{350}}=7.17

c) ME=2.58\frac{52}{\sqrt{100}}=13.42

d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

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".  

Part a

\bar X=21 represent the sample mean  

\mu population mean (variable of interest)  

\sigma=52 represent the population standard deviation  

n=350 represent the sample size  

99% confidence interval  

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

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)  

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: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=2.58  

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

21-2.58\frac{52}{\sqrt{350}}=13.83  

21+2.58\frac{52}{\sqrt{350}}=28.17  

So on this case the 99% confidence interval would be given by (13.83;28.17)  

Part b

The margin of error is given by:

ME=2.58\frac{52}{\sqrt{350}}=7.17

Part c

The margin of error is given by:

ME=2.58\frac{52}{\sqrt{100}}=13.42

Part d

As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:

D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

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s<c

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