Answer :
The probability that a lightbulb will last between 2638 and 2949 hours is approximately 0.8084.
To solve this problem, you can use the normal distribution formula to calculate the probability that a lightbulb will last between 2638 and 2949 hours:
P(2638 < x < 2949) = P(z1 < (x - mean)/standard deviation < z2)
Where x is the number of hours that the lightbulb lasts, mean is the average number of hours that the lightbulb lasts (2872 hours in this case), and the standard deviation is the standard deviation of the number of hours that the lightbulb lasts (108 hours in this case), z1 is the standard normal deviate corresponding to the lower bound of the interval (2638 hours in this case), and z2 is the standard normal deviate corresponding to the upper bound of the interval (2949 hours in this case).
To calculate z1 and z2, you can use the following formulas:
z1 = (2638 - 2872)/108 = -1.22
z2 = (2949 - 2872)/108 = 0.85
To calculate the probability, you can use a normal distribution calculator or table to find the probability that a standard normal random variable is between -1.22 and 0.85.
Using a normal distribution calculator or table, you can find that the probability that a lightbulb will last between 2638 and 2949 hours is approximately 0.8084.
To learn more about probability, refer:-
https://brainly.com/question/22414768
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