Question

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

Answer 1

Answer:

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.