Question

The useful life of an electrical component has a standard deviation of 38.0 hours. If a sample of 35 light bulbs of this type is to be taken, find to two places of decimal the probability that the sample mean useful life, x̄, will be less than 10.0 hours from the true value, μ.

Answer 1

Answer: The useful life of an electrical component has a standard deviation of 38.0 hours. If a sample of 35 light bulbs of this type is to be taken, find to two places of decimal the probability that the sample mean useful life, x̄, will be less than 10.0 hours from the true value, μ.

Solution:

n = 35

σ = 38

the probability that the sample mean useful life, x̄, will be less than 10.0 hours from the true value, μ.

P(x̄-μ < 10) = P((x̄-μ)/σ/√n < 10/σ/√n)

= P(Z < 10/38/√35)

= P(Z < 1.56)

= 0.94062

≈ 0.94

Therefore, the probability that the sample mean useful life, x̄, will be less than 10.0 hours from the true value, μ would be 0.94.