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Stevbo Stevbo
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Posts: 100
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7 years ago
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The mean weight of loads of coal placed in train cars by a loading machine is 43.0 tons with a standard deviation of 8.0 tons. Assuming that the weight of loads placed in the train cars by this loader are normally distributed, if a random sample of 9 loads is chosen for a weight check, find the probability that the mean weight of those loads is more than 40.60 tons.
 
Place your answer, rounded to four decimal places, in the blank.   
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Valued Member
Educator
7 years ago
mean of the sample means: 43 tons

std of the sample means: 8/sqrt(9) = 8/3

t(40.6) = (40.6-43)/(8/3) = -0.9

P(x-bar > 40.6) = P(t > -0.9 when df = 8) = tcdf(-0.9,100,8) = 0.8028
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