SOLUTION: (I only need help on 3 and 4) Tanker trucks are designed to carry huge quantities of gasoline from refineries to filling stations. A factory that manufactures the tank of the truc

Question 1108609: (I only need help on 3 and 4)
Tanker trucks are designed to carry huge quantities of gasoline from refineries to filling stations. A factory that manufactures the tank of the trucks claims to manufacture tanks with a capacity of 8550 gallons of gasoline. The actual capacity of the tanks is normally distributed with mean μ=8544 gallons and standard deviation σ=12 gallons.
1) Find the z-score corresponding to a tank with a capacity of 8550 gallons. Round your answer to one decimal place. =.5
2)What is the probability that a randomly selected tank will have a capacity of less than 8550 gallons? =.691
3)A simple random sample of n = 20 tanks will be selected. Find the z-score corresponding to a sample mean capacity for 20 tanks of 8550. Round your answer to three decimal places. =?
4)A simple random sample of n = 50 tanks will be selected. What is the probability that the mean capacity for these 50 tanks will be greater than 8540 gallons? Round your answer to three decimal places. =?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(I only need help on 3 and 4)
Tanker trucks are designed to carry huge quantities of gasoline from refineries to filling stations. A factory that manufactures the tank of the trucks claims to manufacture tanks with a capacity of 8550 gallons of gasoline. The actual capacity of the tanks is normally distributed with mean μ=8544 gallons and standard deviation σ=12 gallons.
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3)A simple random sample of n = 20 tanks will be selected. Find the z-score corresponding to a sample mean capacity for 20 tanks of 8550. Round your answer to three decimal places. =?
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mean of the sample means = mean of the population = 8550
std of the sample means = (std of the population)/sqrt(sample size)
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# 3:: The z-score of the mean is zero
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4)A simple random sample of n = 50 tanks will be selected. What is the probability that the mean capacity for these 50 tanks will be greater than 8540 gallons? Round your answer to three decimal places.
z(8540) = (8540-8550)/(12/sqrt(50)) = -0.1179
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Cheers,
Stan H.
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