A company receives light bulbs from two different suppliers. Define the variables x and y as x = lifetime of a bulb from Supplier 1
y = lifetime of a bulb from Supplier 2
Five hundred bulbs from each supplier are tested, and the lifetime of each bulb (in hours) is recorded. The density histograms below are constructed from these two sets of observations. Although these histograms are constructed using data from only 500 bulbs, they can be considered approximations to the corresponding probability distributions.
a. Which probability distribution has the larger mean?
b. Which probability distribution has the larger standard deviation?
c. Assuming that the cost of the light bulbs is the same for both suppliers, which supplier would you recommend? Explain.
d. One of the two distributions pictured has a mean of approximately 1,000, and the other has a mean of about 900. Which of these is the mean of the distribution for the variable x (lifetime for a bulb from Supplier 1)?
e. One of the two distributions pictured has a standard deviation of approximately 100, and the other has a standard deviation of about 175. Which of these is the standard deviation of the distribution for the variable x (lifetime for a bulb from Supplier 1)?