In 1998, Mark McGwire of the St. Louis Cardinals hit 70 home runs,a new major le

Question

In 1998, Mark McGwire of the St. Louis Cardinals hit 70 home runs,a new major league record at the time. Was this feat as surprisingas most of us thought? In the three seasons before 1998, McGwirehit a home run in 11.6% of his times at bat. He went to bat 509times in 1998. If he continues his past performance, McGwire's homerun count in 509 times at bat can be modeled as a binomialdistribution with n = 509 and p = 0.116.

Use the binomial distribution to find the probability that McGwirehits 70 or more home runs.

Explanation / Answer

X~Binomial(509,0.116) Since n=509 is large, we can use normal approximation. X~Normal(59.4, 7.22) =np=509*0.116=59.04 =np(1-p)=509*0.116*(1-0.116)=7.22 The probability is P(X>=70)=P((X-)/ >=(70-59.4)/7.22)=P(Z>=1.47)=1-P(Z

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