1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
olga_2 [115]
2 years ago
6

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

that you study a simple random sample of 80 professional basketball games and find that 52 of them are won by the home team. Assuming that there is no home court advantage and that the home team therefore wins 50% of its games in the long run, determine the probability that the home team would win 65% or more of its games in a simple random sample of 80 games
Mathematics
1 answer:
spayn [35]2 years ago
7 0

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

You might be interested in
Which of the following functions is graphed below.
Valentin [98]

Answer: Option A

y=\left \{ {{x^2 +2;\ \ x

Step-by-step explanation:

In the graph we have a piecewise function composed of a parabola and a line.

The parabola has the vertex in the point (0, 2) and cuts the y-axis in y = 2.

The equation of this parabola is y = x ^ 2 +2

Then we have an equation liney = -x + 2


Note that the interval in which the parabola is defined is from -∞ to x = 1. Note that the parabola does not include the point x = 1 because it is marked with an empty circle " о ."

(this is x< 1)

Then the equation of the line goes from x = 1 to ∞ . In this case, the line includes x = 1 because the point at the end of the line is represented by a full circle .

(this is x\geq 1)

Then the function is:

y=\left \{ {{x^2 +2;\ \ x

7 0
3 years ago
When calculating for volume, you use the area of the 2D shape. <br><br> True or false.
Nana76 [90]

Answer:

I think true.

Step-by-step explanation:

Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height.

5 0
3 years ago
Read 2 more answers
The principal of a large high school wants to learn about student opinion regarding remote learning versus in person learning. E
jasenka [17]

Answer:

Step-by-step explanation:

the students that are in the survey are in it because they like the subject, rather than picking students from both types of groups, the ones that aren't doing remote learning and the ones that are doing remote learning.

6 0
3 years ago
Solve for X in the rectangle?
Brilliant_brown [7]

Answer:

x=6

Step-by-step explanation:

13x+12=90

13x=78

x=6

6 0
3 years ago
Read 2 more answers
Judy bought her tent on sale. The sale price was $70 off the original price. Judy also used a coupon for an extra $15 off. If Ju
kifflom [539]
125+15+70=210 your answer is 210
7 0
3 years ago
Other questions:
  • 99-97+95-93+....+7-5+3-1
    5·2 answers
  • Rule that allows financial institutions to calculate simple interest using 360 days in a year is called
    10·2 answers
  • Write an inequality to represent the following scenario: Hagrid’s goal at the National Hotdog Eating Contest is to consume 32 ho
    12·2 answers
  • Tony runs a pizza parlor. His daily cost for operating the restaurant consists of a constant cost of $75 for rent, employee wage
    8·2 answers
  • Plz let me know if yes or no, and plz explain!!!
    9·2 answers
  • Calculate the length of side AC:
    7·1 answer
  • What is the area of the real bedroom?
    9·2 answers
  • Check weather 9.6. 15.10 are in proportion ?​
    8·1 answer
  • X and Y intercepts of y=1/3x
    14·1 answer
  • One cubic meter represents a cube shape that measures 1 meter in all three dimensions. how long is each side in centimeters?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!