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4 years ago

Becky d james have a total of 4 2/8 feet of yarn. Becky has 1 5/8 feet of yarn. How many feet of yarn does james have?

1 answer:

7 0

Let
x----------------> feet of yarn of Becky
y----------------> feet of yarn of James

we know that
4 2/8------> 4 1/4--------> (4*4+1)/4-----> 17/4
1 5/8------> (1*8+5)/8-----> 13/5
x+y=4 2/8-------> x+y=17/4----> equation 1
x=1 5/8--------> x=13/5------> equation 2
substitute 2 in 1
[13/5]+y=17/4------> y=(17/4)-(13/5)----> y=[5*17-4*13]/20
y=(85-52)/20-----> y=33/20----> y=1.65-----> y=1 65/100----> y=1 13/20

the answer is
james have 1 13/20 ft of yarn

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$\= x = 18.5$ , $\sigma = 5.15$

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From the question we are are told that

The sample data is 21, 14, 13, 24, 17, 22, 25, 12

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$\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}$

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Given that the confidence level is 90% then the significance level is evaluated as

$\alpha = 100-90$

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$Z_{\frac{ \alpha }{2} } = 1.645$

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$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

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=> $E = 2.995$

The 90% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

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$18.5 - 2.995 < \mu < 18.5 + 2.995$

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considering part c

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$\alpha = 100-95$

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$Z_{\frac{ \alpha }{2} } = 1.96$

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$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

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$\= x - E < \mu < \= x + E$

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$18.5 - 3.569 < \mu < 18.5 + 3.569$

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