5. Norma LeDist, chief engineer for Brightwell Electric, knows that the lifetimes of light bulbs are normally distributed with mean 1000 hours and standard deviation 100 hours. (a) Sketch the distribution of light bulb lifetimes. What is the label for the X-axis of this distribution? (b) Shade the region of this distribution corre-sponding to light bulbs that have a lifetime shorter than 900 hours. By eyeball, what percentage of bulbs have a lifetime shorter than 900 hours?

6. (Exercise 5 continued) Norma's light bulbs come in four-packs, and we can assume that the four bulbs in each pack constitute a random sample of size four from the light bulb population. Now sup-pose we choose 100 four-packs at random, and for each pack we measure the lifetime of each of the four bulbs and compute the mean of the four. (a) Sketch the distribution of mean bulb lifetimes for these four-packs. What is the label for the X-axis of this distribution? Is it the same as the label in Exercise 5(a)? If so, why? If not, why not? (b) What is the mean of this distribution of means? Is it the same as the mean in Exercise 5? If so, why? If not, why not? (c) What is the standard deviation of this distribution of means called? What is its magnitude? Is this magnitude the same as the standard deviation in Exercise 5? If so, why? If not, why not?

CAN YOU ANSWER 6 AND SHOW THE SKETCH