SOLUTION: The Federal Reserve reports that the mean lifespan of a five dollar bill is 4.9 years. Let�s suppose that the standard deviation is 1.9 years and that the distribution of lifespa

Question 1128016: The Federal Reserve reports that the mean lifespan of a five dollar bill is 4.9 years. Let�s suppose that the standard deviation is 1.9 years and that the distribution of lifespans is normal
Find:
(a) the probability that a $5 bill will last more than 4 years.
(b) the probability that a $5 bill will last between 3 and 5 years.
(c) the 97th percentile for the lifespan of these bills (a time such that 97% of bills last less than that time).
(d ) the probability that a random sample of 37 bills has a mean lifespan of more than 4.5 years.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd
a. z=(4-4.9)/1.9=-0.47
probability z>-0.47 is 0.6808
b. this is a z between -1.9/1.9 or -1 and .1/1.9 or 0.05
probability is z between -1 and 0.05, or 0.3613
c. 97th percentile is z>1.88
1.88=(x-4.9)/1.9
=8.47 years
d. This is a z> (4.5-4.9)/1.9/sqrt(35), sampling distribution of sample means.
z> -0.4*sqrt(35)/1.9=-1.25
probability is 0.8944

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