Answer to Question #263957 in Statistics and Probability for sab

Question #263957

An electric 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:

a. Greater than 1 150 hours?

b. Less than 1 250 hours ?

c. Between 1 150 and 1 250 hours?


1
Expert's answer
2021-11-11T14:13:37-0500

"\\mu=1200 \\\\\n\n\\sigma = 250 \\\\\n\nn=100"

a.

"P(\\bar{x} > 1150) = 1 -P(\\bar{x} < 1150) \\\\\n\n= 1 -P(Z< \\frac{1150-1200}{250 \/ \\sqrt{100}} )\\\\\n\n= 1 -P(Z< -2) \\\\\n\n= 1 -0.0227 \\\\\n\n= 0.9773"

b.

"P(\\bar{x} < 1250) = P(Z < \\frac{1250-1200}{250 \/ \\sqrt{100}}) \\\\\n\n= P(Z< 2) \\\\\n\n= 0.9772"

c.

"P(1150 < \\bar{x} < 1250) = P(\\bar{x} < 1250) -P(\\bar{x} < 1150) \\\\\n\n= P(Z < \\frac{1250-1200}{250 \/ \\sqrt{100}}) -P(Z < \\frac{1150-1200}{250 \/ \\sqrt{100}}) \\\\\n\n= P(Z< 2) -P(Z< -2) \\\\\n\n= 0.9772 -0.0227 \\\\\n\n= 0.9545"


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