If light bulbs are normally distributed with a mean of 2500 hrs. and a standard deviation of 500 hrs. what percentage of light bulbs have a life span less than 2500 hrs.?
z = (score -mean)/sd
z = (2500 -2500)/500
z = 0 is 50%
23
To find the percentage of light bulbs that have a life span less than 2500 hours, we need to use a normal distribution table or a statistical calculator.
Step 1: Standardize the value
The first step is to standardize the value of 2500 hours using the formula:
z = (x - μ) / σ
Where:
z is the standardized value
x is the given value (2500 hours)
μ is the mean (2500 hours)
σ is the standard deviation (500 hours)
Plugging in the values:
z = (2500 - 2500) / 500
z = 0
Step 2: Look up the z-score
Next, we need to look up the z-score in a standard normal distribution table. The table provides the area under the curve to the left of a given z-score.
Since the z-score is 0, the area to the left of this z-score is 0.5 or 50%.
Step 3: Calculate the percentage
Since the area under the curve to the left of the standardized value represents the percentage of light bulbs with a life span less than 2500 hours, the answer is 50%.
Therefore, 50% of the light bulbs have a life span less than 2500 hours.