David V. answered • 6d

Chemical Engineer PhD with 9+ Years of Industrial Experience

This problem tells us that the distribution of weekly wages at the factory is normally shaped, so 68.2% of wages fall within +/- 1 standard deviation of the mean. Since the mean is $400, this means that 68.2% of wages fall between $400 +/- $50, or between $350-$450.

Instead, we are interested in the probability of a wage being between $350-$400. Said differently, this is between the mean ($400) and one standard deviation below the mean ($350). The fact that the wages are normally distributed also means that the shape of the distribution is symmetrical above and below the mean. So the probability of wages being between $350-$400 is half of 68.2%, or 34.1%.