The lifespan of light bulbs is approximately normally distributed. Some statistics about lifespans of two different types of light bulbs are listed.

• LED bulbs: mean: 2,300 days, standard deviation: 230 days
• Incandescent bulbs: mean: 100 days, standard deviation: 10 days

To estimate the proportion of bulbs that burn out in a certain interval of time, use technology to find the area under the normal curve and above the appropriate interval.

1. Estimate the proportion of LED bulbs that are expected to burn out before getting within 1 standard deviation of the mean (before 2,070 days).

2. Estimate the proportion of incandescent bulbs that are expected to burn out before getting within 1 standard deviation of the mean (before 90 days).

3. Estimate the proportion of LED bulbs that are expected to burn out after getting more than 1 standard deviation greater than the mean (after 2,530 days).

4. Estimate the proportion of incandescent bulbs that are expected to burn out after getting more than 1 standard deviation greater than the mean (after 110 days).

5. Estimate the proportion of LED bulbs that are expected to burn out in the interval between 1 standard deviation less than the mean and 1 standard deviation greater than the mean (between 2,070 and 2,530 days).

6. Estimate the proportion of incandescent bulbs expected to burn out in the interval between 1 standard deviation less than the mean and 1 standard deviation greater than the mean (between 90 and 110 days).

7. Estimate the proportion of LED bulbs that are expected to burn out in the interval between 2 standard deviations less than the mean and 2 standard deviations greater than the mean (between 1,840 and 2,760 days).

8. Estimate the proportion of LED bulbs that are expected to burn out in the interval between 1,900 days and 2,100 days.

9. Estimate the proportion of incandescent bulbs that are expected to burn out in the interval between 107 and 118 days.

The wait times at a popular restaurant are approximately normally distributed. The mean wait time is 24.3 minutes with a standard deviation of 3.2 minutes.

Use technology to estimate the wait times for the described groups of customers.

1. Describe the number of minutes customers have to wait if their wait times are in the longest 10% of wait times for customers at this restaurant.

2. Describe the number of minutes customers have to wait if their wait times are in the shortest 15% of wait times for customers at this restaurant.

3. To find the wait times for the middle 50% of wait times for customers:

   1. Draw an example of a normal distribution, and shade approximately the middle 50% of the area under the curve.

   2. What percentage of the total area is the unshaded region to the left of the region you shaded? What value marks the line between the unshaded and shaded parts?
   3. What percentage of the total area is the unshaded region to the right of the region you shaded? What value marks the line between the unshaded and shaded parts?

   4. The shaded region is between which two values?

4. The customers who have wait times in the middle 70% are between which two values?