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Manufacturing and Product Development

Diningroom chairs come in many different woods, styles, and shapes. The height of the seat of a randomly selected oak dining-room chair is approximately normal with mean 85 centimeters (cm) and standard deviation 1.88 cm.

a. Find a value h such that 99% of all dining-room chairs have height less than h.

b. Consumer testing indicates that any chair seat higher than 90 cm is uncomfortable to use when eating. What is the probability that a randomly selected dining-room chair is uncomfortable?

c. Find the first and third quartiles of the dining-room chair height distribution.

d. There is some evidence to suggest that, after five years of use, the mean height of these chairs has decreased, due to wear, erosion, and humidity. Suppose that after five years, the probability the height is more than 86 cm is 0.0718. Find the mean height after five years.

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