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?
"\\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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