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True [87]
3 years ago
8

Which statement below correctly depicts the expected value of a fair game?

Mathematics
2 answers:
nydimaria [60]3 years ago
6 0

Answer:

Step-by-step explanation:

First of all it is important to know about the fair game.  A game is said to be fair if it has equal chances of winning for both the parties.

In Statistical terms, this can be said as expected value =0

If E(X) = 1 where X is from the player, then organizer of the game would have more chances of losing.

Similarly if E(X)>0where X is from the player, then organizer of the game would have more chances of losing.

Also if E(X)>1, where X is from the player, then organizer of the game would have more chances of losing.

Hence a fair game is one where

E(X) =0

Mnenie [13.5K]3 years ago
3 0
E(x)=0 will be your answer

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a) 68% probability that the sample mean will be within ±5 of the population mean.

b) 95% probability that the sample mean will be within ±10 of the population mean.

Step-by-step explanation:

To solve this problem, we have to understand the Empirical Rule and the Central Limit Theorem

Empirical Rule

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Central Limit Theorem

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 s= \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

Mean: \mu = 200

Standard deviation of the population: \sigma = 50

Size of the sample: n = 100

Standard deviation for the sample mean: s = \frac{50}{\sqrt{100}} = 5

a.What is the probability that the sample mean will be within ±5 of the population mean?

5 is one standard deviation from the mean.

By the Empirical Rule, 68% probability that the sample mean will be within ±5 of the population mean.

b.What is the probability that the sample mean will be within ±10 of the population mean?

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