Question #334079

2. An electrical company claims that the average life of the bulbs it manufactures is 1 200 hours with a standard deviation of 250 hours. If a random sample of 100 bulbs is chosen, what is the probability that the sample mean will be less than 1150 hours? (5 points)


a. Z = - 2

b. Z = - 3

c. Z = - 4

d. Z = - 5


1
Expert's answer
2022-04-27T16:24:32-0400

Let X=X= the sample mean: XN(μ,σ2/n)X\sim N(\mu,\sigma^2/n)


P(X<1150)=P(Z<11501200250/100)P(X<1150)=P(Z<\dfrac{1150-1200}{250/\sqrt{100}})

=P(Z<2)0.022750=P(Z<-2)\approx0.022750


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