1Final averages are typically apploximately normally distrib

1)Final averages are typically apploximately normally distributed with a mean of 72 and a standard deviation of 12.5. Your professor says that the top 8% of the class will receive an A, the next 20% a B, the next 42% a C, the next 18% a D, and the bottom 12% an F.

a) what average would you need to receive an \"A\"

b) what average would you need to receive a grade better than a C?

c) what average must you obtian to pass the course? (you\'ll need a D or better)

2.) Speeds of individual cars are 62 mph

a) find standard deviation of all speeds if 3% of cars travel faster than 72 mph

b) using the standard deviation found in part a, find the percentage of these cars that are traveling slower than 55 mph.

c) using the standard deviation found in part a find the 95th percentile for the variable \"speed\"

3) the weighs of ripe watermelons grown at Mr. Smith\'s farm are normally distributed with a standard deviation of 2.8 IB Find the mean weight of Mr. Smithsripe watermelons if only 3% weigh less than 15 ib

4) a machine fills containers with a mean weight per container of 16.0 oz. If no more than 5% of the containers are to weigh less than 15.8 oz, what must the standard deviation of the weights equal? (assume normality)

Solution

A) P(z>Z) = 0.08
then P((mark-72)/12.5 > Z) = 0.08
then (mark-72)/12.5 = 1.405
then mark = 89.6

B) P(z>Z) = 0.70
then P((mark-72)/12.5 > Z) = 0.70
then (mark-72)/12.5 = -0.525
then mark = 65.4

C) P(z>Z) = 0.70
then P((mark-72)/12.5 > Z) = 0.88
then (mark-72)/12.5 = -1.175
then mark = 57.3