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3 years ago

Which equation represents this situation?

Mathematics

1 answer:

aalyn [17]3 years ago

7 0

Answer:

dirk =13.25 hours

charlie =11 75 hours

Step-by-step explanation:

c+d=25------(1)

d-1.5=c-----(2)

from (1),

c+d=25

c=25-d-----(3)

substitude (3) into (2)

d-1.5=c

d-1.5=25-d

2d=26.5

d=13.25

if d=13.25 hours

c+d=25

c+13.25=25

c=25-13.25

c=11.75

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Here for constructing 96% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

So, 96% confidence interval for the population mean, $\mu$ is ;

P(-2.114 < $t_1_0_0$ < 2.114) = 0.96 {As the critical value of t at 100 degree

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P(-2.114 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.114) = 0.96

P( $-2.114 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.114 \times {\frac{s}{\sqrt{n} } }$ ) = 0.96

P( $\bar X-2.114 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.114 \times {\frac{s}{\sqrt{n} } }$ ) = 0.96

96% confidence interval for $\mu$ = [ $\bar X-2.114 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.114 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $55-2.114 \times {\frac{3.4}{\sqrt{101} } }$ , $55+2.114 \times {\frac{3.4}{\sqrt{101} } }$ ]

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Therefore, 96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

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