PLEASE HELP ME!!<br> (Geometry)

Consider the question of whether the home team wins more than half of its games in the National Basketball Association. Suppose

spayn [35]

Answer:

0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games

Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

The home team therefore wins 50% of its games

This means that $p = 0.5$

Determine the probability that the home team would win 65% or more of its games in a simple random sample of 80 games

Sample of 80 means that $n = 80$ and, by the Central Limit Theorem:

$\mu = p = 0.65$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5*0.5}{80}} = 0.0559$

This probability is 1 subtracted by the pvalue of Z when X = 0.65. So

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

By the Central Limit Theorem

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

$Z = \frac{0.65 - 0.5}{0.0559}$

$Z = 2.68$

$Z = 2.68$ has a pvalue of 0.9963

1 - 0.9963 = 0.0037

0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games

7 0

2 years ago

A grocery store chain has been tracking data on the number of shoppers that use coupons. the data shows that 71% of all shoppers

sashaice [31]

The confidence interval comes out to be (0.685,0.735).

Calculating the Confidence Level and Other Terms

The confidence level can be calculated as follows,

z = $\frac{36}{40} * 100%$ %

z = 90 %

The margin error is given as, E= 0.025

The p value in this case is 0.71

Calculating the Confidence Interval

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.

Confidence interval can be obtained by using the following formula,

(p-E, p+E) = (0.71-0.025, 0.71+0.025).

Therefore, the confidence interval is (0.685, 0.735).

Learn more about confidence interval here:

brainly.com/question/24131141

#SPJ4

3 0

1 year ago

Is this equation an identity?<br> -7 + 7g = -10 + 7g + 3

djverab [1.8K]

Answer: i dont really know if im right but here! :L

Step-by-step explanation: Now, say G is an Abelian group, finitely generated from generator In this sense abelian groups are “more interesting” than vector spaces. and in the table below, the second last column is the identity, while the last column is cyclic of order 4, with 9g the generator

7 0

2 years ago

If tan e = 1.3, what is the value of cot (90° - 9)?

ella [17]

Answer:

A

Step-by-step explanation:

We are given that:

$\tan(\theta)=1.3$

And we want to find:

$\cot(90^\circ -\theta)$

Remember that tangent and cotangent are co-functions. In other words, they follow the cofunction identities:

$\tan(\theta)=\cot(90^\circ-\theta)\text{ and } \cot(90^\circ-\theta)=\tan(\theta)$

Therefore, since tan(θ) = 1.3 and cot(90° - θ) = tan(θ), then cot(90° - θ) must also be 1.3.

Our answer is A.

7 0

3 years ago

the shaded area of the following shape can be found by subtracting the area of the circle from the area of the triangle?

balu736 [363]

I found the accompanying picture of this word problem.

The circle was inscribe in the triangle. The area outside of the circle but inside the triangle is the shaded area.

True. The shaded area of the following shape can be found by subtracting the area of the circle from the area of the triangle.

7 0

3 years ago

PLEASE HELP ME!! (Geometry)