SOLUTION: 1. A manufacturer of light bulbs produces bulbs that last a mean of 1050 hours with a standard deviation of 100 hours. What is the probability that the mean lifetime of a random sa

Question 1174178: 1. A manufacturer of light bulbs produces bulbs that last a mean of 1050 hours with a standard deviation of 100 hours. What is the probability that the mean lifetime of a random sample of 10 of these bulbs is greater than 975 hours?
2. The average public high school has 535 students with a standard deviation of 98.
a. If a public school is selected, what is the probability that the number of students enrolled is less than 550?
b. If a random sample of 25 public high schools is selected, what is the probability that the number of the students enrolled is greater than 600?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd/sqrt(n)
> = (975-1050/100/sqrt(10) or -75*sqrt(10)/100 or z>= -2.37
probability is 0.9911
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z < (550-535)/98 or < 15/98=0.15
that probability is 0.5596
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I assume the question means what is the probability that the mean enrollment of these 25 schools is > 600.
This is z > (600-535)/98/sqrt(25) or z > 65/19.6 or > 3.32
that probability is 0.00045 or 0.0005.

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