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iren [92.7K]
2 years ago
8

A small community organization consists of 20 families, of which 4 have one child,8 have two children, 5 have three children, 2

have four children, and 1 has fivechildren. If one of these families is chosen at random, what is the probability it has`children,`= 1,2,3,4,5?
Mathematics
1 answer:
ELEN [110]2 years ago
3 0

Answer and Step-by-step explanation:

According to the situation, The probabilities for each one is given below:

As there are 20 families

So the probabilities for each one is

For four families have one child is

= \frac{4}{20}\\\\ = \frac{1}{5}

For eight families have two children is

= \frac{8}{20}\\\\ = \frac{2}{5}

For five families have three children is

= \frac{5}{20}\\\\ = \frac{1}{4}

For two families have four children is

= \frac{2}{20}\\\\ = \frac{1}{10}

For one family have five children is

= \frac{1}{20}

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A researcher is testing how bacterial cells react to different environments. She placed a petri dish that initially had 32,000 b
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<u>Solution- </u>

A researcher placed a petri dish with 32,000 bacterial cells. One hour after being placed in the vacuum chamber, the number of cells in the petri dish had halved. Another hour later, the number of cells had again halved.

This can be represented as exponential decreasing function,

y=a(1 - r)^x

Where,

  • a = starting amount  = 32000
  • r = rate  = 50% = 0.5 as the sample becomes halved in each hour
  • x = hours

Putting the values,

\Rightarrow y=32000(1 - 0.5)^x

\Rightarrow y=32000(0.5)^x

y-intercept means, where x=0, so

\Rightarrow y=32000(0.5)^0\\\\\Rightarrow y=32000\times 1=32000

The coordinate of this poin will be (0, 32000)

This means when x=0 or at the starting of the research, the number of bacteria cells was 32000.

After 3 hours, number of bacteria cells will be,

\Rightarrow y=32000(0.5)^3

\Rightarrow y=32000\times 0.125

\Rightarrow y=4000

The  coordinate of this point will be (3, 4000)

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2 years ago
If Johnny had 20 complete living room outfits, disregard color scheme, how many different sets of five complete outfits could be
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Employees in the marketing department of a large regional restaurant chain are researching the amount of money that households i
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Answer:

The <em>z</em>-score for the group "25 to 34" is 0.37 and the <em>z</em>-score for the group "45 to 54" is 0.25.

Step-by-step explanation:

The data provided is as follows:

25 to 34              45 to 54

  1329                    2268

  1906                    1965

 2426                     1149

  1826                     1591

  1239                    1682

   1514                     1851

  1937                     1367

  1454                    2158

Compute the mean and standard deviation for the group "25 to 34" as follows:

\bar x=\frac{1}{n}\sum x=\frac{1}{8}\times [1329+1906+...+1454]=\frac{13631}{8}=1703.875\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{8-1}\times 1086710.875}=394.01

Compute the <em>z</em>-score for the group "25 to 34" as follows:

z=\frac{x-\bar x}{s}=\frac{1851-1703.875}{394.01}=0.3734\approx 0.37

Compute the mean and standard deviation for the group "45 to 54" as follows:

\bar x=\frac{1}{n}\sum x=\frac{1}{8}\times [2268+1965+...+2158]=\frac{14031}{8}=1753.875\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{8-1}\times 1028888.875}=383.39

Compute the <em>z</em>-score for the group "45 to 54" as follows:

z=\frac{x-\bar x}{s}=\frac{1851-1753.875}{383.39}=0.25333\approx 0.25

Thus, the <em>z</em>-score for the group "25 to 34" is 0.37 and the <em>z</em>-score for the group "45 to 54" is 0.25.

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