A hot dog eating contest was held at baruch. The mean number of hotdogs eaten wa

Question

A hot dog eating contest was held at baruch. The mean number of hotdogs eaten was 25 and the standard deviation was 3. a) What percentage of participants ate less than 24 hot dogs? b) What percentage of participants ate more than 30 hot dogs? c) What percentage of participants ate less than 29 hot dogs? d) What percentage of participants ate more than 23 and 29 hot dogs? e) What percentage of participants ate between 23 and 29 hot dogs? f) What percentage of participants ate between 28 and 32 hot dogs?

Explanation / Answer

a)P(X<24)=P(Z<(24-25)/3)=P(Z<-0.3333)=0.3694~36.94%

b)P(X>30)=1-P(X<30)=1-P(Z<1.6667)=1-0.9522=0.0478=~4.78%

c)P(X<29)=P(Z<1.3333)=0.9088~90.88%

d)P(X>23)&P(X>29)=P(X>29)=1-P(X<29)=1-0.9088=0.0912~9.12%

e)P(23<X<29)=P(-0.6667<Z<1.3333)=0.9088-0.2525=0.6563~65.63%

f)P(28<X<32)=P(1<Z<2.3333)=0.9902-0.8413=0.1488~14.88%

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