Answer to Question #178244 in Statistics and Probability for Roy Teodoro

Question #178244

a manufacturer of light bulbs produces bulbs that last a mean of 950 hours with a standard deviation of 12 hours what is the probability that the mean lifetime of the random sample of 10 of these bulbs is less than 90 hours


1
Expert's answer
2021-04-15T06:57:38-0400

"\\text{let X a random variable showing the life of an incandescent lamp in hours }"

"\\mu= 950;\\sigma=" 12

"X\u223cN(\u03bc,\u03c3^2\/n)"

"Z= \\frac{X-\\mu}{\\sigma\/\\sqrt{n}}"

"P(X<90)=P(Z<\\frac{90-950}{12\/\\sqrt{10}})=P(Z<-226)=0"

Answer: 0 is probability that the mean lifetime of the random sample of 10 of these bulbs is less than 90 hours



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