Question

With the diagrams please

4. 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 2.1 years and that the distribution of lifespans is normal (not unreasonable!)

Find: (a) the probability that a $5 bill will last more than 4 years.

(b) the probability that a $5 bill will last between 5 and 7 years.

(c) the 94^th percentile for the lifespan of these bills (a time such that 94% of bills last less than that time).

(d ) the probability that a random sample of 37 bills has a mean lifespan of more than 5.1 years.

DON'T FORGET THE DIAGRAMS, PLEASE

Answer 1

4

This is a normal distribution question with


a)
P(x > 4.0)=?
The z-score at x = 4.0 is,

This implies that



b)
P(5.0 < x < 7.0)=?

This implies that

PS: you have to refer z score table to find the final probabilities.

c)
we know, value less than 94th percentile will have a corresponding z score value = 1.5548
P(z < 1.5548) = 0.94

d)
This is a normal distribution question with


a)
P(x > 5.1)=?
The z-score at x = 5.1 is,

This implies that

PS: you have to refer z score table to find the final probabilities.


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