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2 years ago

Joan wants to jog 15 miles on a circular track 1/2 mile a diameter

Mathematics

1 answer:

skad [1K]2 years ago

4 0

Answer:

7.5

Step-by-step explanation:

15/2

2 doesn't go into 1 so go over to the 15 and then 7 goes into 15 two times do subtract 15 and 14 and then you'll get one once you have 1 left over add a decimal next to the 7 on top right after that add a 0 next to the one then you'll get a 10 once you have a 10, you can know how much 2 goes into 10 which 5 and subtract 10 by it self then you'll get your answer 7.5

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Answer:

$0.82-2.977\frac{0.048}{\sqrt{15}}=0.783$

$0.82+2.977\frac{0.048}{\sqrt{15}}=0.857$

So on this case the 99% confidence interval would be given by (0.783;0.857)

So then we can conclude that at 99% of confidence the true mean is between (0.783;0.857) and the specification is satisfied since the value of 0.8 is on the confidence interval

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".

$\bar X= 0.82$ represent the sample mean

$\mu$ population mean (variable of interest)

s=0.048 represent the sample standard deviation

n=15 represent the sample size

Solution to the problem

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 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 $t_{\alpha/2}=2.977$

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

$0.82-2.977\frac{0.048}{\sqrt{15}}=0.783$

$0.82+2.977\frac{0.048}{\sqrt{15}}=0.857$

So on this case the 99% confidence interval would be given by (0.783;0.857)

So then we can conclude that at 99% of confidence the true mean is between (0.783;0.857) and the specification is satisfied since the value of 0.8 is on the confidence interval

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