Question

In: Math

4. The Federal Reserve reports that the mean lifespan of a five dollar bill is 4.9...

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 1.9 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 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.

Solutions

Expert Solution

4)

Solution :

Given that ,

mean = = 4.9

standard deviation = = 1.9

(a)

P(x > 4) = 1 - P(x < 4)

= 1 - P((x - ) / < (4 - 4.9) / 1.9)

= 1 - P(z < -0.4737)

= 1 - 0.3179

= 0.6821

P(x > 4) = 0.6821

Probability = 0.6821

(b)

P(3 < x < 5) = P((3 - 4.9)/ 1.9) < (x - ) / < (5 - 4.9) / 1.9) )

= P(-1 < z < 0.0526)

= P(z < 0.0526) - P(z < -1)

= 0.521 - 0.1587

= 0.3623

Probability = 0.3623

(c)

P(Z < z) = 97%

P(Z < 1.88) = 0.97

z = 1.88

Using z-score formula,

x = z * +

x = 1.88 * 1.9 + 4.9 = 8.472

97th percentile = 8.472

(d)

n = 37

= 4.9 and

= / n = 1.9 / 37 = 0.3126

P( > 4.5) = 1 - P( < 4.5)

= 1 - P(( - ) / < (4.5 - 4.9) / 0.3126)

= 1 - P(z < -1.28)

= 1 - 0.1003

= 0.8997

P( >4.5) = 0.8997

Probability = 0.8997


Related Solutions

4. The Federal Reserve reports that the mean lifespan of a five dollar bill is 4.9...
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 1.9 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 3 and 5 years. (c) the 90th percentile for the lifespan of these bills (a time such that 90% of...
4. The Federal Reserve reports that the mean lifespan of a five dollar bill is 4.9...
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 1.9 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 3 and 5 years. (c) the 90th percentile for the lifespan of these bills (a time such that 90% of...
The Federal Reserve reports that the mean lifespan of a five dollar bill is 4.9 years....
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 94th percentile for the lifespan of these bills (a time such that 94% of bills...
With the diagrams please 4. The Federal Reserve reports that the mean lifespan of a five...
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 94th percentile for the lifespan of these bills (a time...
Draw a labeled diagram of the normal distribution The Federal Reserve reports that the mean lifespan...
Draw a labeled diagram of the normal distribution 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 94th percentile for the lifespan of these bills...
An urn contains 3 ​one-dollar bills, 1​ five-dollar bill and 1​ ten-dollar bill. A player draws...
An urn contains 3 ​one-dollar bills, 1​ five-dollar bill and 1​ ten-dollar bill. A player draws bills one at a time without replacement from the urn until a​ ten-dollar bill is drawn. Then the game stops. All bills are kept by the player.​ Determine: ​(A)  The probability of winning ​$11 . ​(B)  The probability of winning all bills in the urn. ​(C)  The probability of the game stopping at the second draw.
4.If a six-month Treasury bill is purchased for $0.9475 on a dollar (i.e., $94,750 for a...
4.If a six-month Treasury bill is purchased for $0.9475 on a dollar (i.e., $94,750 for a $100,000 bill), what is the discount yield, the annual rate of interest, and the compound rate? What will these yields be if the discount price falls to $0.924 on a dollar (i.e., $92,400 for a $100,000 bill)? PLEASE SHOW WORK
4. The Federal Reserve and the money supply Suppose the money supply (as measured by checkable...
4. The Federal Reserve and the money supply Suppose the money supply (as measured by checkable deposits) is currently $300 billion. The required reserve ratio is 25%. Banks hold $75 billion in reserves, so there are no excess reserves. The Federal Reserve ("the Fed") wants to decrease the money supply by $32 billion, to $268 billion. It could do this through open-market operations or by changing the required reserve ratio. Assume for this question that you can use the oversimplified...
9) Explain the 4 methods that the Federal Reserve uses to manage money supply in the...
9) Explain the 4 methods that the Federal Reserve uses to manage money supply in the U.S. economy.   (10pts) 10)   Explain the 3 Dow Jones Averages. How is the Dow Jones Industrial Average calculated daily? Explain why the Dow Jones Industrial Average is important to investors in the U.S. and around the world.       (10pts)
1) Explain the 4 ways the Federal Reserve would increase the money Supply and explain and...
1) Explain the 4 ways the Federal Reserve would increase the money Supply and explain and graph how this would impact interest rates, consumption, investment, AD, GDP, Prices and Unemployment. (Make sure to include both the money and the goods graph).
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT