Suppose that you are designing an instrument panel for a large industrial machine. The initial design of the machine requires the person using it to be able to reach 700 mm from a particular position. The reach for adult women from this position is known to have a mean of 800 mm with a standard deviation of 100 mm. The reach for adult men is known to have a mean of 900 mm with a standard deviation of 100 mm. Both women’s and men’s reach from this position is normally distributed. c) If you were to redesign this equipment, how close would you have to make the parts to be reached in order to ensure that only 2% of women would be unable to use it?

To determine how close the parts need to be made for the equipment to be used by 98% of women, we need to find the value that corresponds to the 98th percentile of the normal distribution of women's reach from this position. We can use the z-score formula to convert this percentile to a standard score (z-score): z = (x - μ) / σ where x is the value we want to find, μ is the mean of women's reach (800 mm), and σ is the standard deviation of women's reach (100 mm). To find the z-score for the 98th percentile, we can use a standard normal distribution table or calculator, which gives us a z-score of 2.05. Thus, we can solve for x: 2.05 = (x - 800) / 100 x - 800 = 205 x = 1005 mm Therefore, to ensure that only 2% of women would be unable to use the equipment, the parts that need to be reached should be no farther than 1005 mm from the starting position.