Question

weight of men is normal distributed with mean of 185 lb and standard deviation of 39 lb. A water taxi that holds 30 passengers has a maximum capacity of 6000 lb. If taxi is fully loaded with men, what is the probability that it goes over the maximum capacity? Round to 4 decimal places.

Answer #1

average capacity for a man =6000/30 =200

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

here mean= μ= | 185 |

std deviation =σ= | 39.0000 |

sample size =n= | 30 |

std error=σ_{x̅}=σ/√n= |
7.1204 |

probability that it goes over the maximum capacity:

probability = | P(X>200) | = | P(Z>2.11)= | 1-P(Z<2.11)= | 1-0.9826= |
0.0174 |

( please try 0.0176 if this comes wrong due to rounding)

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