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vovangra [49]
3 years ago
8

<, =, or >? -9/2 ? -4 1/2

Mathematics
1 answer:
astra-53 [7]3 years ago
8 0
Less than right? Because it’s a negative?
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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
How do I round to the nearest cent with this number? 0.19125
LekaFEV [45]

Answer: 0.19

Step-by-step explanation: Rounding to the nearest cent is the same as rounding to the nearest hundredth

5 0
3 years ago
Read 2 more answers
If f(x) = 2x - 6 and g(x) = 3x + 9, find (f - g)(x).
Shalnov [3]
The answer will be C
3 0
3 years ago
The temperature was 38 degrees Fahrenheit before a cold front came through. Ten hours later, the temperature was -12 degrees Fah
padilas [110]

Answer:

-5 degrees per hour

Step-by-step explanation:

In 10 hours, the temperature dropped -50 degrees (38 + 12, and make it negative because the temperature went down, not up).

So divide -50 by 10

-50/10 = -5

7 0
2 years ago
Please helpppppp meeee
yKpoI14uk [10]

Answer:

0.25     Converges

Step-by-step explanation:

First, we need to expand our series so that we get the following:

\sum _{n=1}^{\infty \:}\frac{n}{4^n}+\frac{1}{4^{n+1}}

We can then use the series ratio test on each term. (L < 1 = absolutely convergent)

\sum _{n=1}^{\infty \:}\frac{n}{4^n}

\lim_{n \to \infty} \frac{n}{4^{n}\\} =

⇒  converges

\sum _{n=1}^{\infty \:}\frac{1}{4^n^+1}

\lim_{n \to \infty} \frac{n}{4^{n}^+1\\}

⇒  converges

converges + converges

= converges

~Hope this helps! Once again, sorry if my explanation is a bit confusing~

8 0
3 years ago
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