The Citiburg Parks Department has just installed 1100 new lightbulbs with an expected mean lifespan of 64 months and a lifespan standard deviation of 8 months. Assuming normally distributed bulb failure, how many bulbs will need to be replaced after 49 months? Round your answer to the nearest whole number.
Please help, I'm having trouble solving this using the excel format they've given and I just can't get it.
Z = (score-mean)/SEm
SEm = SD/√n
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. Multiply by 1100.
To solve this problem using Excel, you can utilize the concept of the normal distribution and the Z-score formula. Here are the steps to find the number of bulbs that need to be replaced after 49 months:
1. Open Excel and create a new worksheet.
2. In cell A1, enter the mean lifespan of the lightbulbs, which is 64 months.
3. In cell A2, enter the standard deviation of the lightbulbs' lifespan, which is 8 months.
4. In cell A3, enter the number of months after which you want to calculate the number of bulbs to be replaced, which is 49 months.
5. In cell A4, enter the formula "= (A3 - A1) / A2" to calculate the Z-score. This formula subtracts the mean (A1) from the given time (A3) and then divides it by the standard deviation (A2).
6. In cell A5, enter the formula "=NORM.DIST(A4,0,1,TRUE)" to calculate the probability of a bulb failing before the given time. This formula uses the NORM.DIST function to find the cumulative probability of the Z-score (A4) assuming a standard normal distribution with a mean of 0 and a standard deviation of 1.
7. In cell A6, enter the formula "= A5 * 1100" to calculate the number of bulbs that are expected to fail before the given time. This formula multiplies the calculated probability (A5) by the total number of bulbs installed (1100).
8. Finally, format cell A6 as a whole number to round the result to the nearest whole number. To do this, right-click on cell A6, select "Format Cells," go to the "Number" tab, and choose the "Number" category without decimal places.
After following these steps, cell A6 should display the number of bulbs that need to be replaced after 49 months, rounded to the nearest whole number.
If you are still having trouble, please provide the specific issue you are facing, and I'll be glad to assist you further.