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2 years ago

Randomly meeting a four child family with either one or exactly 2 boy children

Mathematics

1 answer:

Lelechka [254]2 years ago

3 0

Answer:

The probability of randomly meeting a four child family with either exactly one or exactly two boy children = (5/8) = 0.625

Step-by-step explanation:

Complete Question

The probability of randomly meeting a four child family with either exactly one or exactly two boy children.

Solution

The possible sample spaces for a family with four children include

4 boys and 0 Girl

BBBB

3 boys and 1 girl

BBBG BBGB BGBB GBBB

2 boys and 2 girls

BBGG BGBG BGGB GBBG GBGB GGBB

1 boy and 3 girls

BGGG GBGG GGBG GGGB

0 boy and 4 girls

GGGG

Total number of elements in the sample space = 16

Probability of an event is defined as the number of elements in that event divided by the Total number of elements in the sample space.

The required probability is a sum of probabilities.

The probability of meeting a four child family with exactly 1 boy = (4/16) = (1/4) = 0.25

The probability of meeting a four child family with exactly 2 boys = (6/16) = (3/8) = 0.375

The probability of randomly meeting a four child family with either exactly one or exactly two boy children = (4/16) + (6/16) = (10/16) = (5/8) = 0.25 + 0.375 = 0.625

Hope this Helps!!!

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Lera25 [3.4K]

Answer:

The correct option is A

Step-by-step explanation:

From the question we are told that

The population is $\mu = 6.6$

The level of significance is $\alpha = 5\% = 0.05$

The sample data is 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds

The Null hypothesis is $H_o : \mu = 6.6$

The Alternative hypothesis is $H_a : \mu > 6.6$

The critical value of the level of significance obtained from the normal distribution table is

$Z_{\alpha } = Z_{0.05 } = 1.645$

Generally the sample mean is mathematically evaluated as

$\=x = \frac{\sum x_i }{n}$

substituting values

$\=x = \frac{9.0 + 7.3 + 6.0+ 8.8+ 6.8+ 8.4+6.6 }{7}$

$\=x = 7.5571$

The standard deviation is mathematically evaluated as

$\sigma = \sqrt{\frac{\sum [ x - \= x ]}{n} }$

substituting values

$\sigma = \sqrt{\frac{ [ 9.0-7.5571]^2 + [7.3 -7.5571]^2 + [6.0-7.5571]^2 + [8.8- 7.5571]^2 + [6.8- 7.5571]^2 + [8.4 - 7.5571]^2+ [6.6- 7.5571]^2 }{7} }$ $\sigma = 1.1774$

Generally the test statistic is mathematically evaluated as

$t = \frac{\= x - \mu } { \frac{\sigma }{\sqrt{n} } }$

substituting values

$t = \frac{7.5571 - 6.6 } { \frac{1.1774 }{\sqrt{7} } }$

$t = 1.4274$

Looking at the value of t and $Z_{\alpha }$ we see that $t < Z_{\alpha }$ hence we fail to reject the null hypothesis

What this implies is that there is no sufficient evidence to state that the sample data show as significant increase in the average birth rate

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2 years ago

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2. Consider traiangle AED. F is mipoint of AE and G is midpoint of DE, then FG is midline of triangle AED. This means that

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3. Consider trapezoid BFGC. Its area is

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