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Tpy6a [65]
2 years ago
9

Focus groups of 15 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number

(per group) who recognize the Yummy brand name is 12.5, and the standard deviation is 0.58. Would it be unusual to randomly select 15 people and find that fewer than 9 recognize the Yummy brand name?
Mathematics
1 answer:
Morgarella [4.7K]2 years ago
6 0

Answer:

Yes, 15 people would be unusual as it falls outside of 2 standard deviation of mean.

Step-by-step explanation:

Consider the provided information.

The mean number (per group) who recognize the Yummy brand name is 12.5, and the standard deviation is 0.58.

Mean = μ= 12.5  

σ = 0.58

n = 15

\mu\pm2\sigma=12.5\pm 2(0.58)\\\mu\pm2\sigma=12.5\pm1.16\\\mu\pm2\sigma=[11.34, 13.66]

Yes, 15 people would be unusual as it falls outside of 2 standard deviation of mean.

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\bf 0.580\overline{80}\implies \boxed{\cfrac{5.80\overline{80}}{10}}\qquad \textit{now, let's say }x= 5.80\overline{80}\\\\
-------------------------------

\bf thus\qquad \begin{array}{llll}
100\cdot x&=&580.80\overline{80}\\
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&&575+x
\end{array}\qquad \implies 100x=575+x
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99x=575\implies x=\cfrac{575}{99}\qquad therefore\qquad \boxed{\cfrac{5.80\overline{80}}{10}}\implies \cfrac{\quad \frac{575}{99}\quad }{10}
\\\\\\
\cfrac{\quad \frac{575}{99}\quad }{\frac{10}{1}}\implies \cfrac{575}{99}\cdot \cfrac{1}{10}\implies \cfrac{575}{990}\implies \stackrel{simplified}{\cfrac{115}{198}}

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4 0
2 years ago
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A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity. When the tank is placed upright
pentagon [3]

Answer:

2.12 ft above ground level

Step-by-step explanation:

Volume of the cylindrical tank is 36*π

Tank is filled to half its capacity, that means tank is filled 18*π, and level of water is 4 feet, then the height of the cylinder is 8 feet

With the above information we can calculate the radius of the base of the cylinder, according to

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Then the radius of the base is  2.12 ft

When the cylindrical tank is place on its side, the level of water inside have to be 2.12 ft above ground level. That is the level of half its capacity

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Here, we want to write out the two numbers from the information in the question

Firstly, the two numbers are greater than 10

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The correct answers here are 21 and 28

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