The lifetime of a certain brand of tire is normally distributed with a mean of

1. The lifetime of a certain brand of tire is normally distributed with a mean of 80,000 km. and standard deviation of 7,000 km. The tire carries a warranty for 68,000 km.
a) What is the probability that the tire you recently purchased will last at most 81,000 km.?    
If you made this selection, what would be your probability of losing money?   
If you made this choice, what would be the probability of making more than 3% ?   [removed]

5. In the movie Forest Gump, the public school required an IQ of at least 70 to be admitted.
a) If IQ test scores are normally distributed with a mean of 100 and a standard deviation of 17, what percent of children would qualify for admittance to the school?  [removed] % format{~.dd}
b) If the public school wished to have 85% of all children qualify for admittance, what minimum IQ test score should be required for admittance?   [removed] format{ ~.d}

6. At a certain university the cumulative grade point average (CGPA) of first year students usually averages 2.81 with a standard deviation 0.56 . It has been found that the marks are usually approximately normally distributed. 
a) What is the probability that a student will have a CGPA that is between 1 and 3 ?   [removed]
b) What percent of students will be on probation, i.e. their CGPA is less than 2 ?   [removed] % format{~.dd}
c) Academic scholarships are awarded to the top 2% of first year students. What minimum CGPA is needed to receive a scholarship?  [removed] format{ ~.d}