normal distribution

Question

Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $50. Find the probability that a worker selected at random makes between $300 and $350.

Answer 1

The range of 300-350 is 50-100 away from the mean of 400. Since the standard deviation is 50, we are looking at 1-2 standard deviations from the mean. Statistical tables show 34.1% is the distribution in one direction from 0-1 std devs, and 13.6% from 1-2. Therefore, the answer is 13.6%.