Question 1081199: The average number of mosquitos in a stagnant pond is 80 per square meter with a standard deviation of 12. If 36 square meters are chosen at random for a mosquito count, find the probability that the average of those counts is more than 81.8 mosquitos per square meter. Assume that the variable is normally distributed.
0.3%
31.6%
81.6%
18.4%
The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 40% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 18 adult dogs is studied. What is the probability that no more than 3 of them weigh 65 lb or more?
0.0082
0.0328
0.9672
0.9918
In a survey of 305 registered voters, 130 of them wished to see Mayor Waffleskate lose her next election. Construct a 95% confidence interval for the proportion of registered voter who want to see Mayor Waffleskate defeated.
0.380 < p < 0.473
0.398 < p < 0.455
0.317 < p < 0.535
0.371 < p < 0.482
A study of 65 bolts of carpet showed that their average length was 74.2 yards. The standard deviation of the population is 3.6 yards. Which of the following is the confidence interval for the mean length per bolt of carpet?
73.3 < μ < 75.1
73.2 < μ < 75.2
72.1 < μ < 76.3
73.7 < μ < 74.7
A simple random sample of kitchen toasters is to be taken to determine the mean operational lifetime in hours. Assume that the lifetimes are normally distributed with population standard deviation hours.
Find the sample size needed so that a confidence interval for the mean lifetime will have a margin of error of 8.
117
34
5
6
thank you
Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! t=(81.8-80)/12/sqrt (36)
1.8*6/12=0.9
I want the probability that a t df=35 is >0.9 which is 0.1871. If I use a z, I get 0.184, so 18.4%
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look at 0 of them which is .6^18=0.0001
1 of them which is 18*0.6^17*0.4=0.0012
2 of them which is 18C2=153*0.6^16*0.4^2=0.007
3 of them which is 18C3=816*0.6^15*0.4^3=0.0246. They add to 0.033 or 3.3%, the second choice
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The interval is 1.96 SE =1.96*sqrt (p*(1-p)/n)=1.96* sqrt (.426*.574/305)=0.056 on either side of 0.426
(0.370, 0.481), the last choice.
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The last one is a CI for a z-test. The % is not stated--will assume 95%
(73.32, 75.08), the first choice.
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The last one can't be done without more information.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! The average number of mosquitos in a stagnant pond is 80 per square meter with a standard deviation of 12. If 36 square meters are chosen at random for a mosquito count, find the probability that the average of those counts is more than 81.8 mosquitos per square meter. Assume that the variable is normally distributed.
z(81.8) = (81.8-80)/(12/sqrt(36)) = 1.8/2 = 0.9
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P(x-bar > 81.8) = P(z > 0.9) = 18.4%
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The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 40% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 18 adult dogs is studied. What is the probability that no more than 3 of them weigh 65 lb or more?
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Binomial Problem with n = 3 and p(>= 65) = 0.4
P(0<= x <=3) = binomcdf(18,0.4,3) = 0.9328
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In a survey of 305 registered voters, 130 of them wished to see Mayor Waffleskate lose her next election. Construct a 95% confidence interval for the proportion of registered voter who want to see Mayor Waffleskate defeated.
p-hat = 130/305 = 0.426
ME = 1.96*sqrt(0.426*0.574/305) = 0.055
95% CI:: 0.426-0.055 < p < 0.426+0.055
95% CI:: 0.371 < p < 0.482
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A study of 65 bolts of carpet showed that their average length was 74.2 yards. The standard deviation of the population is 3.6 yards. Which of the following is the confidence interval for the mean length per bolt of carpet?
Find the sample mean
Find the Margin of Error
Follow the example above.
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A simple random sample of kitchen toasters is to be taken to determine the mean operational lifetime in hours. Assume that the lifetimes are normally distributed with population standard deviation hours.
Find the sample size needed so that a confidence interval for the mean lifetime will have a margin of error of 8.
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Insufficient information.
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117
34
5
6
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Cheers,
Stan H.
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