Lifespan

The lifetime of a light bulb is a random variable with a normal distribution of x = 300 hours, σ = 35 hours.
a) What is the probability that a randomly selected light bulb will have a lifespan of more than 320 hours?
b) Up to what value of L hours can the lamp life be expected to last longer than L hours with a probability of 0.25?

Correct result:

p =  0.284
L =  323.6 h

Solution:

μ=300 h σ=35 h  x...N(μ,σ) t>320 h  p=0.2839=0.284μ=300 \ \text{h} \ \\ σ=35 \ \text{h} \ \\ \ \\ x ... N(μ,σ) \ \\ t > 320 \ h \ \\ \ \\ p=0.2839=0.284
L=323.6=16185=323.6 hL=323.6=\dfrac{ 1618 }{ 5 }=323.6 \ \text{h}



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