Question 184727: Iam am taking statistics and I am having trouble with my homework.
Normal Distributions: Finding Values
1. Answer the questions about the specified normal distribution.
a.The lifetime of ZZZ batteries are normally distributed with a mean of 270 hours and a standard deviation of 10 hours. Find the number of hours that represent the the 40th percentile.
b.Scores on an English placement test are normally distributed with a mean of 55 and standard deviation of 6.5. Find the score that marks the top 5%.
Sampling Distribution and the Central Limit Theorem
2. Find the probabilities.
a.From National Weather Service records, the annual snowfall in the TopKick Mountains has a mean of 92 inches and a standard deviation of 12 inches. If the snowfall from 36 randomly selected years are chosen, what it the probability that the snowfall would be less than 95 inches?
b. The loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 60. If 49 applicants are randomly chosen, what is the probability that they will have a rating between 230 and 260? Round z scores to two decimal places.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Answer the questions about the specified normal distribution.
a.The lifetime of ZZZ batteries are normally distributed with a mean of 270 hours and a standard deviation of 10 hours. Find the number of hours that represent the the 40th percentile.
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Hopefully you have a TI calculator with STAT functions and/or a z-chart.
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Draw the normal curve; put 270 in for the mean; note that s = 10
Shade a left tail that has 40% of the population in it.
You want the x-value that separates 40% left from 60% right.
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Using a TI you use InvNorm(0.4,270,10) to get 267.47 hrs.
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b.Scores on an English placement test are normally distributed with a mean of 55 and standard deviation of 6.5. Find the score that marks the top 5%.
Sampling Distribution and the Central Limit Theorem
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InvNorm(0.95,55,6.5) = 65.69
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2. Find the probabilities.
a.From National Weather Service records, the annual snowfall in the TopKick Mountains has a mean of 92 inches and a standard deviation of 12 inches. If the snowfall from 36 randomly selected years are chosen, what is the probability that the snowfall would be less than 95 inches?
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Sketch a normal curve; label the horizontal axis as "sample mean";
let the mean be 92 inches; the standard deviation is 12/sqrt(36) = 2
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Find the area to the left of 95.
Using a TI you get P(0 < x < 95) = normalcdf(0,95,92,2) = 0.93319..
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b. The loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 60. If 49 applicants are randomly chosen, what is the probability that they will have a rating between 230 and 260? Round z scores to two decimal places.
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Again, the horizontal axis is "sample mean"; mean = 240; stdev = 60/sqrt(49)
= 60/7 = 8.57
Shade the area under the curve between x = 230 and x = 260
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Using a TI you get: P(230 < x < 260) = normalcdf(230,260,240,60/7)= 0.8685..
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Cheers,
Stan H.
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