QUESTION 3 An Australian airline has determined that after fuel and baggage, the

Question

QUESTION 3 An Australian airline has determined that after fuel and baggage, the plane can accommodate no more than 85 kg per person to be below its maximum take-off weight. The average weight of Australians is 78.5 kg with a standard deviation of 10.2 kg. Express your answers to four decimal places (ie. 90.25% is 0.9025). What is the probability that a randomly selected Australian is above 85 kg? If the plane holds 15 people, what is the probability that the sample average of a full plane exceeds 85 kg? If the plane holds 30 people, what is the probability that the sample average of a full plane exceeds 85 kg?

Explanation / Answer

given standard devaition = 10.2 VALUES ARE TAKEN FROM STANDARD Z TABLE

a) P(X>85) =P(Z> 85-78.5 / 10.2) =P(Z>0.6372)= 0.7357

B) P(X^>85)=P(Z>( 85-78.5 ) / (10.2 /SQRT15) = P(Z>2.2787) =0.9884

C) P(X^85) = P(Z>(85-75)/ ( 10.2/SQRT30) = P(Z>3.4903) =0.9998

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