In a test on electrical bulbs, it was found that the life of a particular make is normally distributed with an average life time of 2040 hours and Standard deviation of 40 hours. Estimate the number of bulbs likely to burn for more than 2140 hours in a sample of 2000 bulbs
To estimate the number of bulbs likely to burn for more than 2140 hours, we first need to find the z-score for 2140 hours using the formula:
z = (X - μ) / σ
Where:
X = 2140 hours
μ = 2040 hours
σ = 40 hours
z = (2140 - 2040) / 40
z = 100 / 40
z = 2.5
Next, we can use the z-score to find the probability of a bulb burning for more than 2140 hours by referring to the standard normal distribution table. From the table, we can see that the probability of the z-score being greater than 2.5 is approximately 0.0062.
Now, we can estimate the number of bulbs likely to burn for more than 2140 hours in a sample of 2000 bulbs by multiplying the probability by the sample size:
Number of bulbs = 0.0062 * 2000
Number of bulbs = 12.4
Therefore, we can estimate that approximately 12 bulbs out of 2000 are likely to burn for more than 2140 hours.