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Levart [38]
3 years ago
13

Before a chair manufacturer sells its beanbag chairs, they spot check a random sample of chairs on the production line. The tabl

e below shows the number of common problems found during one such spot check. Common Problems Frequency Open seam 4 Cuts in upholstery 14 Understuffed 15 None 267 Total 300 If the manufacturer makes 1500 beanbag chairs per day, how many of those chairs would they expect to be understuffed?
Mathematics
2 answers:
Colt1911 [192]3 years ago
7 0

Answer:

They would expect 75 chairs to be understuffed.

Step-by-step explanation:

fenix001 [56]3 years ago
6 0

Answer:

75

Step-by-step explanation:

Given :   In beanbags

             4 Cuts in upholstery

            15 are Understuffed  

             None 267

            Total 300

To Find : If the manufacturer makes 1500 beanbag chairs per day, how many of those chairs would they expect to be understuffed?

Solution :

We are given that out of total of 300 bags there are 15 understuffed

Let x be the no. of understuffed bean bags out of total of 1500.

⇒\frac{15}{300} =\frac{x}{1500}

⇒\frac{15*1500}{300} =x

⇒75=x

Thus  If the manufacturer makes 1500 beanbag chairs per day, 75 of those chairs would they expect to be understuffed .


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(-2,7) (1,10) (2,27)
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Mystery Boxes: Breakout Rooms
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Answer:

\begin{array}{ccccccccccccccc}{1} & {3} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {57} & {58} & {61} \\ \end{array}

Step-by-step explanation:

Given

\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {[ \ ]} \\ \end{array}

Required

Fill in the box

From the question, the range is:

Range = 60

Range is calculated as:

Range =  Highest - Least

From the box, we have:

Least = 1

So:

60 = Highest  - 1

Highest = 60 +1

Highest = 61

The box, becomes:

\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}

From the question:

IQR = 20 --- interquartile range

This is calculated as:

IQR = Q_3 - Q_1

Q_3 is the median of the upper half while Q_1 is the median of the lower half.

So, we need to split the given boxes into two equal halves (7 each)

<u>Lower half:</u>

\begin{array}{ccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } \\ \end{array}

<u>Upper half</u>

<u></u>\begin{array}{ccccccc}{[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}<u></u>

The quartile is calculated by calculating the median for each of the above halves is calculated as:

Median = \frac{N + 1}{2}th

Where N = 7

So, we have:

Median = \frac{7 + 1}{2}th = \frac{8}{2}th = 4th

So,

Q_3 = 4th item of the upper halves

Q_1= 4th item of the lower halves

From the upper halves

<u></u>\begin{array}{ccccccc}{[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}<u></u>

<u></u>

We have:

Q_3 = 32

Q_1 can not be determined from the lower halves because the 4th item is missing.

So, we make use of:

IQR = Q_3 - Q_1

Where Q_3 = 32 and IQR = 20

So:

20 = 32 - Q_1

Q_1 = 32 - 20

Q_1 = 12

So, the lower half becomes:

<u>Lower half:</u>

\begin{array}{ccccccc}{1} & {[ \ ]} & {4} & {12 } & {15} & {18}& {[ \ ] } \\ \end{array}

From this, the updated values of the box is:

\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}

From the question, the median is:

Median = 22 and N = 14

To calculate the median, we make use of:

Median = \frac{N + 1}{2}th

Median = \frac{14 + 1}{2}th

Median = \frac{15}{2}th

Median = 7.5th

This means that, the median is the average of the 7th and 8th items.

The 7th and 8th items are blanks.

However, from the question; the mode is:

Mode = 18

Since the values of the box are in increasing order and the average of 18 and 18 do not equal 22 (i.e. the median), then the 7th item is:

7th = 18

The 8th item is calculated as thus:

Median = \frac{1}{2}(7th + 8th)

22= \frac{1}{2}(18 + 8th)

Multiply through by 2

44 = 18 + 8th

8th = 44 - 18

8th = 26

The updated values of the box is:

\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}

From the question.

Mean = 26

Mean is calculated as:

Mean = \frac{\sum x}{n}

So, we have:

26= \frac{1 + 2nd + 4 + 12 + 15 + 18 + 18 + 26 + 29 + 30 + 32 + 12th + 58 + 61}{14}

Collect like terms

26= \frac{ 2nd + 12th+1 + 4 + 12 + 15 + 18 + 18 + 26 + 29 + 30 + 32 + 58 + 61}{14}

26= \frac{ 2nd + 12th+304}{14}

Multiply through by 14

14 * 26= 2nd + 12th+304

364= 2nd + 12th+304

This gives:

2nd + 12th = 364 - 304

2nd + 12th = 60

From the updated box,

\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}

We know that:

<em>The 2nd value can only be either 2 or 3</em>

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Of these values, the only possible values of 2nd and 12th that give a sum of 60 are:

2nd = 3

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2nd + 12th = 60

3 + 57 = 60

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\begin{array}{ccccccccccccccc}{1} & {3} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {57} & {58} & {61} \\ \end{array}

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