Question

A certain baseball player hits a home run in 7% of his at-bats. Consider his at-bats as independent events. Find the probability that this baseball player hits at most 42 home runs in 800 at-bats?

0.0307

0.9693

0.93

0.07

Answer #1

here for binomial distribution parameter n=800 and p=0.07 |

here mean of distribution=μ=np= | 56.00 | |

and standard deviation σ=sqrt(np(1-p))= | 7.22 | |

for normal distribution z score =(X-μ)/σx | ||

since np and n(1-p) both are greater than 5, we can use normal approximation of binomial distribution |

probability that this baseball player hits at most 42 home runs in 800 at-bats :

probability
=P(X<42.5)=(Z<(42.5-56)/7.217)=P(Z<-1.87)=0.0307 |

A
certain baseball player hits a home run in 7% of his at-bats.
Consider his at-bats as independent events. Find the probability
that this baseball player hits more than 42 home runs in 800
at-bats?
a) 0.93
b) 0.9693
c) 0.07
d) 0.0307

A certain baseball player hits a home run in 7% of his at bats.
Consider his at bats as independent events. Find the probability
that this baseball player hits more than 42 home runs in 800 at
bats.
Please show work.

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