Probability?

In 1998, Mark McGwire of the St. Louis Cardinals hit 70 home runs, a new Major League record. Was this feat as surprising as most of us thought In thethree seasons before 1998, McGwire hit a home run in 11.6% of his times at bt. He went to bat 509 times at bat has apprximately the binomial dstribution with n=509 and p=0.116.





(a) what is the mean number of home runs McGwire wll hit in 509 times at bat?





(b) What is the probability that he hits 70 or more home runs?





(c) In 2001, Barry Bonds of the San Francisco Giants hit 73 home runs, breaking McGwire's record. This was suprising. n the three previous seasons, Bonds hit a home run in 8.65% of his timesat bat. He batted 476 times in 2001. Considering his home rn counts as a binomial random variable with n=476 and p=0.0865, wat is the probability of 73 or more home runs?

Probability?
Because n is too large, we should use a normal approximation. mean = np=509(0.116)=59.04=59


variance=np(1-p)=509(0.116)(0.884)=52....


Standard deviation s=7.224


b) P(x %26gt; 70) = P( z %26gt; (70-59.04-0.5)/7.224) --- (1)


=P( z %26gt; 1.447)=0.0735 or 7.35 %


Note: A continuity correction 0.5 has been applied in (1).





c)Again, we use a normal approximation


mean =(475)(0.0865)=41.0875=41


variance=(475)(0.0865)(0.9135)=37.533


sd=6.126


P( x%26gt;73) = P( z %26gt; (73-41.0875-0.5)/6.126 )


=P(z %26gt; 5.1) =0 %