# predictions from a normal model (Normal Distribution)

• Apr 20th 2008, 10:28 AM
Desiderius
predictions from a normal model (Normal Distribution)
A.) It was estimated that batting averages in major league baseball in the 1940s were distributed with a mean of 0.260 and a standard deviation of 0.07. What percentage of the batters would have an average greater than 0.400?

B.) Recent estimates have the batting averages distributed with the same mean but less variability. THe new standard deviation is estimated to be 0.05. What percentage of the players would bat over 0.400 today?

Thanks.
• Apr 20th 2008, 06:35 PM
mr fantastic
Quote:

Originally Posted by Desiderius
A.) It was estimated that batting averages in major league baseball in the 1940s were distributed with a mean of 0.260 and a standard deviation of 0.07. What percentage of the batters would have an average greater than 0.400?

B.) Recent estimates have the batting averages distributed with the same mean but less variability. THe new standard deviation is estimated to be 0.05. What percentage of the players would bat over 0.400 today?

Thanks.

A.) Let X be the random variable batting average in the 1940's.
Then X ~ Normal(mean = 0.260, sd = 0.07).
Calculate Pr(X > 0.4000). Multiply the answer by 100 to get %.

B.) Let Y be the random variable contemporary batting average.
Then Y ~ Normal(mean = 0.260, sd = 0.05).
Calculate Pr(Y > 0.4000). Multiply the answer by 100 to get %.

Without knowing how you've been taught to calculate for normal distributions (tables, technology such as TI-84, TI-89, statistics software, on-line probability calculators, numerical integration of the pdf etc.) it's impossible to say much more without wasting time .......