1. Glucose levels in patients free of diabetes are assumed to follow a normal distribution with a mean of 120 and a standard deviation of 16. a) What proportion of patients have glucose levels exceeding 115? b) If a patient has a glucose level of 140, what percentile is this? c) What is the probability that the mean glucose level exceeds 115 in a sample of 12 patients? Solution all answers are from z tables directly. a)0.6227 b)89.44 percentile c)0.8605.

1. 1. Go to the Wall Street Journal webpage http://online.wsj.com/mdc/public/page/2_3020-
treasury.html?mod=topnav_2_3000 and find out the ask/bid price quotes and asked yields for
treasury bills (1) maturing on 2009/09/24, traded on 2008/09/24 (2) maturing on 2010/09/23,
traded on 2009/09/24 (3) maturing on 2011/09/22, traded on 2010/09/24 2. Please use the
“asked” rate to calculate the ask prices for the above three T-bills using bank discount method
(assume time to maturity for each T-bill is one year, that is, you DON’T need to annualize the
rate). 3. Calculate the three annualized bond equivalent yields based on the ask prices calculated
above (assume time to maturity for each T-bill is one year, that is, you DON’T need to annualize
the rate). 4. What trend can you observe from one-year T-bill yields calculated above? List
reasons that could explain the trend.
Solution
(1) Maturing on 2009/09/24 : Assuming Face value of the bill is $ 1,000,000
Current T- Bill Prce = Facce Value (1 - Days to maturity /365 x Discount Yield)
= 1,000,000 (1 - 365/365 x 0.055) = 1000,000 (1- 0.055) = 1,000,000 x
0.945= 1,058,201
Bond Equivalent yield Yield = 365 x Discount Yield/360-Days to Maturity x Discount Yield
BEY = 365 x 0.055/365-365 x 0.055 = 20.075/360 - 20.075 = 20.075/339,925 = 0.0590 or
5.90%
T-Bill Ask Price = Face Value /1+ BEY x Days to Maturity/365 = $ 1,000,000/1+0.0705 x
365/365
= 1,000,000 / 1.0705 = 934,142.92
2. T-Bill maturity date = 2010/9/23 = Assuming Face Value is $ 1,000,000
Current T - Bill Price = Face Value (1- Days to Maturity / 365 x discount yield = 1,000,000(1-
365/365 x 0.123)
= 1,000,000/1 - 1 x 0.123 = 1,000,000 / 0.877 = $ 1,140,250.855
Bond Equivalent Yield (BEY) = 365 x Discount Yield / 365 - Days to Maturity x Discount
Yield
= 365 x 0.123 / 365 - 365 x 0.123 = 44.895 / 365 - 44.895
= 44.895/320.105 = 0.14025 or 14.02%
Bill ask price based on BEY = Face Value/ 1+ BEY x Days to Maturity /365 = $ 1,000,000 /
1+ 0.1402 x 365/365
= 1,000,000/ 1+ 0.1402 = 877,039
3. Maturity Date = 2011/9/22 : Details are not available in the web site