Mathematics, 31.05.2020 06:57 travisvb

A television show tests the abilities of alleged psychics by presenting contestants with a set of
4
44 cards placed upside down,
1
11 of which has a star printed on it. Each contestant attempts to identify which card has the star on it for a series of
50
5050 trials.
Assuming that the contestants are purely guessing, what are the mean and standard deviation of the number of trials where the contestant guesses correctly?

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N = 4 is the overall number of points distributed to the contestant, x = 1 reflects the number of decks with a star on them. The probability of selecting the correct card is as follows:

$\to P(X)=\frac{x}{N}=\frac{1}{4}=0.25$

For a total of n = 50 trials, each competitor must determine whichever card has the star on it.The result of each trial is different from the results of the others.A proper selection of a card with such a star shows the success of each trial.The Binomial distributions can account for such a random value of x, As a result, X has a binomial distribution having values n = 50

and

.The Binomial distribution does have the following mean and standard deviation:

$\to \text{Mean =np}\\\\\to \text{SD}=\sqrt{np(1-p)}\\\\$

Determine the mean difference of the number of tests where the contender correctly guesses:

$\to \text{Mean =np}= 50 \times 0.25= 12.5\\\\$

$\to SD=\sqrt{np(1-p)}$

$=\sqrt{50 \times 0.25 \times (1-0.25)}\\\\=\sqrt{50 \times 0.25 \times (0.75)}\\\\= \sqrt{12.5 \times 0.75}\\\\=\sqrt{9.375}\\\\=3.061$

As just a result, the standard deviation of the number most right guesses by the competitor are $12.50 \ \ and\ \ 3.061$ , correspondingly.

Learn more about the contestant guesses:

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Answer from: s661103

The mean and standard deviation of the number of trials where the contestant guesses correctly are 12.50 and 3.062.

Step-by-step explanation:

Total number of cards presented to the contestants, N = 4.

Number of cards that has a star printed on it is, x = 1.

The probability of selecting the correct card is:

$P(X)=\frac{x}{N}=\frac{1}{4}=0.25$

It is provided that each contestant attempts to identify which card has the star on it for a series of n = 50 trials.

Each trial's outcome is independent of other outcomes.

The success of each trial is denoted by the correct selection of the card with a star.

The random variable X can be explained by the Binomial distribution.

So, X follows a Binomial distribution with parameters n = 50 and p = 0.25.

The mean and standard deviation of a Binomial distribution are:

$\text{Mean}=np\\\\\text{SD}=\sqrt{np(1-p)}$

Compute the mean and standard deviation of the number of trials where the contestant guesses correctly as follows:

$\text{Mean}=np=50\times 0.25=12.50\\\\\text{SD}=\sqrt{np(1-p)}=\sqrt{50\times 0.25\times (1-0.25)}=3.062$

Thus, the mean and standard deviation of the number of trials where the contestant guesses correctly are 12.50 and 3.062.

Answer from: Quest

the image of (6, 9) under a dilation is (4, 6). the scale factor is

b. 2/3

Answer from: Quest

maybe i can

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A television show tests the abilities of alleged psychics by presenting contestants with a set of