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eimsori [14]
3 years ago
9

What is the approximate area of the shaded region

Mathematics
2 answers:
dmitriy555 [2]3 years ago
8 0

ANSWER

The correct answer is

21.5 square centimeters

EXPLANATION

The shaded area is the area of the square minus the area of the Circle.

Area of shaded region

=  {l}^{2}  - \pi \:  {r}^{2}

From the diagram,

l = 10cm

and

r =  \frac{l}{2}  =  \frac{10}{2}  = 5cm

This implies that,

Area of shaded region

=  {10}^{2}  - \pi \times  {5}^{2}

=  100 -25 \pi

\approx21.5 {cm}^{2}

polet [3.4K]3 years ago
8 0

The answer would be 21.5 square centimeters. Hope this helps!

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Answer:

0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.

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To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 75, \sigma = 4, n = 64, s = \frac{4}{\sqrt{64}} = 0.5

Find the probability that the average score of the 64 golfers exceeded 76.

This is 1 subtracted by the pvalue of Z when X = 64.

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

By the Central Limit Theorem

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

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Z = 2

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

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