Final Answer:
The probability that a particular lightbulb will last longer than 1990 hours is 50%.
Step-by-step explanation:
A lightbulb has an average lifespan of 1990 hours with a standard deviation of 191 hours. This means that the lifespan of the lightbulb follows a normal distribution. A normal distribution is a symmetrical, bell-shaped curve where the mean, median, and mode of the data are equal. The probability of any event occurring is determined by the area under the curve within a certain range of values.
In order to calculate the probability of a particular lightbulb lasting longer than 1990 hours, we must first determine the area under the curve from 1990 hours to infinity. This is the area of the right side of the bell curve. To determine this area, we can use the cumulative area function of the normal distribution. The cumulative area function allows us to determine the area under the curve from any point on the x-axis to infinity.
Plugging in the mean (1990 hours) and the standard deviation (191 hours) into the cumulative area function, we get a value of 0.50. This means that the probability of a particular lightbulb lasting longer than 1990 hours is 50%.