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seropon [69]
3 years ago
9

There are $5$ girls and $5$ boys in a chess club. The club holds a round-robin tournament in which every player plays against ev

ery other player exactly once.
If Anita is one of the club members, what fraction of all games at the tournament does Anita play in? Enter your answer as a fraction in simplified form.
Mathematics
1 answer:
ZanzabumX [31]3 years ago
6 0
1/10, because she plays in 10 games out of 100
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A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. Consider the sample m
love history [14]

Answer:

a) The expected value of the sample mean weight is 20.4 pounds.

b)The standard deviation of the sample mean weight is 0.123.

c) There is a 14.46% probability the sample mean weight will be less than 20.27.

d) This value is c = 20.6153.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}.

Problems of normally distributed samples 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.

In this problem, we have that:

A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. This means that \mu = 20.4, \sigma = 1.23

Consider the sample mean weight of 100 watermelons of this variety. This means that n = 100.

a. What is the expected value of the sample mean weight? Give an exact answer.

By the Central Limit Theorem, it is the same as the mean of the population. So the expected value of the sample mean weight is 20.4 pounds.

b. What is the standard deviation of the sample mean weight? Give your answer to four decimal places.

By the Central Limit Theorem, that is:

s = \frac{\sigma}{\sqrt{n}} = \frac{1.23}{\sqrt{100}} = 0.123

The standard deviation of the sample mean weight is 0.123.

c. What is the approximate probability the sample mean weight will be less than 20.27?

This is the pvalue of Z when X = 20.27.

Since we are working with the sample mean, we use s instead of \sigma in the Z score formula

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

Z = \frac{20.27 - 20.4}{0.123}

Z = -1.06

Z = -1.06 has a pvalue of 0.1446.

This means that there is a 14.46% probability the sample mean weight will be less than 20.27.

d. What is the value c such that the approximate probability the sample mean will be less than c is 0.96?

This is the value of X = c that is in the 96th percentile, that is, it's Z score has a pvalue 0.96.

So we use Z = 1.75

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

1.75 = \frac{c - 20.4}{0.123}

c - 20.4 = 0.123*1.75

c = 20.6153

This value is c = 20.6153.

6 0
2 years ago
You know that the battery in your alarm clock is going to run out of power soon. If it runs out within the next 24 hours, what i
aivan3 [116]
The probability of an event is given by the number of favorable outcomes divided by the total number of outcomes. Here the event is the alarm clock running out of power. There are 24 hours during which the power can go out. You are asleep during 8 of these. A "favorable" outcome in this case is the power going out while you are sleeping -- that is, during one of those 8 hours. This makes the probability that the power goes out while you are sleeping 8/24.
3 0
3 years ago
Solve for x x=750+125.75x
olga2289 [7]
X=750+125.75x
subtract to variable (x) on one side
x-125.75x=750+125.75x-125.75x
-124.75x=750
divide -124.75 to get variable (x) by itself
-124.75x/-124.75=750/-124.75
x=-3000/499
or
x=-6 6/499
or
x=-6.01202

7 0
3 years ago
Determine the value of x in the diagram
Sidana [21]

Answer:

3x + x + 3x + x = 360

8x = 360

x = 45

3(45)= 135

Step-by-step explanation:

3 0
3 years ago
Question 5 of 5 Triangle ABC is an equilateral triangle. How many lines of symmetry does triangle ABC have?
lutik1710 [3]
I believe just 1 because an equilateral triangle can only be reflected on one line for the halves to be the same
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