Question 1141505: Given a normal distribution with � = 104 and σ = 25, if you select a sample of n = 25, what is the probability that X bar is
a. less than 94?
b. Between 94 and 95.5?
c. Above 104.4?
d. There is a 68% chance that X bar is above what value?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z=(x bar-mean)/sigma/sqrt(n
a. x < -10/25/5 or z< -2 and probability is 0.0228
b. z between -2 and -8.5*5/25 or -1.69, and that probability is 0.0228
c. above 104.4 is z>0.4*5/25 or z>0.08 or probability 0.4681
d. this is looking for the z value for 0.3200 probability, which is -0.47 (-0.468), and that is
-0.468=(x bar-104/5)
-2.34=x bar-104, so X bar is above 101.66 or 101.7
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