Question

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

Answer 1

Answer:

$P(370.2$

And we can find this probability with this difference:

$P(-0.762$

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:

$X \sim N(420.2,105)$  

Where $\mu=420.2$ and $\sigma=105$

We are interested on this probability

$P(X$

And we can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

And replacing we got:

$P(370.2$

And we can find this probability with this difference:

$P(-0.762$