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Homework help for intro to stats

label Statistics
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Let x1x2, . . . , x100 denote the actual net weights (in pounds) of 100 randomly selected bags of fertilizer. Suppose that the weight of a randomly selected bag has a distribution with mean 50 lb and variance 1 lb2. Let  be the sample mean weight (n = 100).

(a) What is the probability that the sample mean is between 49.85 lb and 50.15 lb? (Round the answer to four decimal places.)
P(49.85 ≤  ≤ 50.15) =  

(b) What is the probability that the sample mean is less than 50 lb?
 
Apr 26th, 2015

a)  Z  for 50.15 lbs =  50.15 - 50 / (1/√100) = 0.15 / 0.1 = 1.5

P(Z=1.5) = 0.9332

Z for 49.85 =  49.85 - 50 / (1/√100) = -0.15 / 0.1 = -1.5

P(Z=-1.5) = 0.0668

P(49.85 <_Z< 50.15) = 0.9332 - 0.0668 = 0.8664

b) 0.5000

Apr 26th, 2015

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Apr 26th, 2015
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Apr 26th, 2015
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