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3 years ago

Use multiplication to solve the proportion. y/9 = 44/54

Mathematics

2 answers:

drek231 [11]3 years ago

5 0

Answer: $y=7\dfrac{1}{3}$ .

Step-by-step explanation:

$\dfrac{y}{9} =\dfrac{44}{54} \\\\y \times 54=44 \times 9\\\\54y=396\\\\54y \div 54=396 \div 54\\\\y=7\dfrac{1}{3}$

QveST [7]3 years ago

3 0

9•44=396
396/54=7.3 repeating
Therefore y=7.33

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We are given that a laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighing. Scale readings in repeated weighing are Normally distributed with mean equal to the true weight of the specimen.

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Firstly, the pivotal quantity for 99% confidence interval for the true mean specimen is given by;

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where, $\bar X$ = sample mean weighing of specimen = $\frac{3.412+3.416+3.414}{3}$ = 3.414 g

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Here for constructing 99% confidence interval we have used z statistics because we know about population standard deviation (sigma).

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P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5% level

of significance are -2.5758 & 2.5758}

P(-2.5758 < $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

P( $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

99% confidence interval for $\mu$ = [ $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $3.414-2.5758 \times {\frac{0.001}{\sqrt{3} } }$ , $3.414+2.5758 \times {\frac{0.001}{\sqrt{3} } }$ ]

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Therefore, 99% confidence interval for this specimen is [3.4125 , 3.4155].

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