Information for Problems 1 - 5: Photoresist isa light sensitive material used in industrial processes likephotolithography and photoengraving to form a patterned coating ona surface. There are two types of photoresists: positive andnegative. A positive photoresist is one in which the portion of thephotoresist that is exposed to light becomes soluble to thephotoresist developer. A negative photoresist is one in which theportion of the photoresist that is exposed to light becomesinsoluble to the photoresist developer. Suppose the thickness,x, of photoresist applied to wafers in semiconductormanufacturing at a particular location on the wafer is uniformlydistributed between 0.2150 and 0.2350 micrometers.
1.    Find theprobability distribution function for x. Â
2.    Find thecumulative distribution function of photoresist thickness.
3.    Determinethe proportion of wafers that exceed 0.2275 micrometers inphotoresist thickness.
4.    What is theminimum thickness that is exceeded by 30% of the wafers? Â
5.    Determinethe mean of the photoresist thickness.
Information for Problems 6 - 10: Cholesterol isa fatty substance that is an important part of the outer lining(membrane) of cells in the body of animals. Its normal range for anadult is 120-240 mg/dl. The Food and Nutrition Institute (FNI) ofthe Philippines found that the total cholesterol level for Filipinoadults has a mean, µ, of 148.9 mg/dl. Furthermore, the FNI reportsthat 92% of adults have a total cholesterol level below 200 mg/dland that total cholesterol level is normally distributed.
6.    What is thestandard deviation of this normal distribution? Give answerto 1 decimal places.
7.    An adult isconsidered to be at high risk for cardiovascular disease if his/hertotal cholesterol level is above 240.8 mg/dl. What proportion ofFilipino adults are at high risk for cardiovascular disease?Give answer to 4 decimal places.
8.    An adult isconsidered to be at moderate risk for cardiovascular disease ifhis/her total cholesterol level is between 200 and 240.8 mg/dl.What proportion of Filipino adults are at moderate risk forcardiovascular disease?  Give answer to 4decimal places.
9.    What is thevalue of total cholesterol level that exceeds 90% of the Filipinopopulation? Give answer to 2 decimal places.
10. Above what total cholesterol valuewill 25% of the Filipino population fall? Give answer to 2decimal places.
Information for Problems 11 - 15: A fiberspinning process currently produces a fiber whose strength isnormally distributed with a mean of 71 N/m2. The minimumacceptable strength is 65N/m2. Give answer to 4decimal places.
11. Ten percent of the fiber producedby the current method fails to meet the minimum specification. Whatis the standard deviation of the fiber strengths in the currentprocess?  Â
12. If the mean remains at71N/m2 and the minimum acceptable strength remains at65N/m2, what must the standard deviation be so that only5% of the fiber will fail to meet the specification?
13. If the mean remains at71N/m2 and the minimum acceptable strength remains at65N/m2, what must the standard deviation be so that only1% of the fiber will fail to meet the specification?
14. If the standard deviation is3N/m2, to what value must the mean be set so that only1% of the fiber will fail to meet the minimum specification of65N/m2?
15. If the standard deviation is3N/m2, to what value must the mean be set so that only2% of the fiber will fail to meet the specification of65N/m2?      Â
