Question

The lifetimes of light bulbs are normally distributed with a mean of 1490 hours and a standard deviation of
150 hours
1. Determine the proportion of light bulbs lasting less than 1380 hours. Round your answer to 4 decimal
places
2. The longest lasting 5 percent of light bulbs last_hours or more. Round your answer to 1 decimal
place
3. The middle 85 percent of light bulbs last between__and_hours. Round your answers to 1
decimal place
4. Determine the proportion of light bulbs lasting between 1310 and 1680 hours. Round your answer to 4
decimal places
5. Determine the proportion of light bulbs lasting more than 1680 hours. Round your answer to 4
decimal places
6. The shortest-lasting 10 percent of light bulbs last hours or less. Round your answer to 1
decimal place

Answer 1

Answer:

1) Proportion of light bulbs lasting less than 1380 hours.

P(X<1380) = 0.2317(4dp)

2)The longest lasting 5% of light bulbs last 1736.7 hours or more

3) The middle 85% of light bulbs last between 1274.1 and 1705.9 hours

4) Proportion of light bulbs lasting between 1310 hours and 1680 hours is 0.7823 (4 dp)

5) Proportion of light bulbs lasting more than 1680 hours is 0.1026(4dp)

6) The shortest lasting 10% of light bulbs last 1297.8 hours.

Explanation:

The calculations are handwritten and attached as files to this solution. Check the files below for all the workings