Question

ASK A QUESTION Weekly wages at a certain factory are normally distributed with s mean of $400 and a standard deviation of $50. Find the probability that a worker selected at random makes between $250 and $300.

Answer 1

Weekly wages are normally distributed with a mean of $400

standard deviation of $50

we are supposed to find the probability that a worker selected at random makes between $250 and $300.

The z-Score can be written as

$z=\frac{x-\mu}{\sigma } \\ \\ z=\frac{300-400}{50}=-2\\ \\ z=\frac{250-400}{50}=-3$

Now as we can write the probability as

$P(-3\leq z\leq -2)=P( z\leq -2)-P( z\leq -3)$

Now using the Z-score table we can write

$P(-3\leq z\leq -2)=0.0227-0.0014\\ \\ P(-3\leq z\leq -2)=0.0213$