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krok68 [10]
3 years ago
12

Can someone help me pls

Mathematics
2 answers:
larisa86 [58]3 years ago
6 0

Answer: A=53.576 degrees

Step-by-step explanation:

Cos A= adjacent/hypt

Cos A= 19/32

Cos A= .59375

inverse of Cos A=.59375

A=53.576 degrees

Sveta_85 [38]3 years ago
4 0

Answer:

A = 53.58°

Step-by-step explanation:

cos A = 19/32

cos A = 0.5938

A = 53.58°

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Answer:

654.16-2.02\frac{165.23}{\sqrt{42}}=602.66    

654.16+2.02\frac{165.23}{\sqrt{42}}=705.66    

So on this case the 95% confidence interval would be given by (602.66;705.66)

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=654.16 represent the sample mean

\mu population mean (variable of interest)

s=165.23 represent the sample standard deviation

n=42 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=42-1=41

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,41)".And we see that t_{\alpha/2}=2.02

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

654.16-2.02\frac{165.23}{\sqrt{42}}=602.66    

654.16+2.02\frac{165.23}{\sqrt{42}}=705.66    

So on this case the 95% confidence interval would be given by (602.66;705.66)    

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