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, <em>N</em> = 4.
Number of cards that has a star printed on it is, <em>x</em> = 1.
The probability of selecting the correct card is:

It is provided that each contestant attempts to identify which card has the star on it for a series of <em>n</em> = 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 <em>X</em> can be explained by the Binomial distribution.
So, <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 50 and <em>p</em> = 0.25.
The mean and standard deviation of a Binomial distribution are:

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

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