Answer: the company should promote 4412 hours for these bulbs.
Step-by-step explanation:
Assuming that the lives of the bulbs are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = lifetime of the bulbs in hours.
µ = mean hours
σ = standard deviation
From the information given,
µ = 4000 hours
σ = 200 hours
If only 2% burn out, then the company would promote 98% would meet the claimed lifetime. Looking at the normal distribution table, the z score corresponding to a probability of 0.98 is 2.06. Therefore,
2.06 = (x - 4000)/200
Cross multiplying, it becomes
200 × 2.06 = (x - 4000)
412 = x - 4000
x = 4000 + 412
x = 4412 hours
