In a Scrabble tournament, the scores were normally distributed and the mean score was 420.2 points with a standard deviation of 105.0 points. What is the probability that the score of a randomly selected competitor differs from the mean score by less than 50 points

And we can find this probability with this difference:

Step-by-step explanation:

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

And we can use the z score formula given by:

And replacing we got:

And we can find this probability with this difference:

1 1/5

step-by-step explanation: