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Darya [45]
1 year ago
10

U can start immediately I already got the answer I just need to see if i got it right and understand

Mathematics
1 answer:
umka21 [38]1 year ago
8 0

ANSWER

80 units²

EXPLANATION

One way to solve this is to find the area of the blue square and the subtract the areas of the red triangles:

The blue square is 12 units long by 12 units wide. Its area is:

A_{\text{square}}=12\times12=144

Then, the area of the big triangle, which has a base 12 units long and a height of 10 units, is:

A_{\text{traingle}1}=\frac{12\times10}{2}=\frac{120}{2}=60

The smaller triangle has a base of 4 units and a heigth of 2 units. Its area is:

A_{\text{triangle}2}=\frac{4\times2}{2}=\frac{8}{2}=4

So the total area of the figure is:

\begin{gathered} A=A_{\text{square}}-A_{triangle1}-A_{triangle2} \\ A=144-60-4 \\ A=80 \end{gathered}

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Using the normal distribution, it is found that there is a 0.0005 = 0.05% probability of getting more than 66 heads.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
  • The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with \mu = np, \sigma = \sqrt{np(1-p)}.

For the binomial distribution, the parameters are given as follows:

n = 100, p = 0.5.

Hence the mean and the standard deviation of the approximation are given as follows:

  • \mu = np = 100(0.5) = 50.
  • \sigma = \sqrt{np(1-p)} = \sqrt{100(0.5)(0.5)} = 5

Using continuity correction, the probability of getting more than 66 heads is P(X > 66 + 0.5) = P(X > 66.5), which is <u>one subtracted by the p-value of Z when X = 66.5</u>.

Z = \frac{X - \mu}{\sigma}

Z = \frac{66.5 - 50}{5}

Z = 3.3

Z = 3.3 has a p-value of 0.9995.

1 - 0.9995 = 0.0005.

0.0005 = 0.05%

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

6 0
1 year ago
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