3. An airline computes the capacity and range for its planes using a normal dist

Question

3. An airline computes the capacity and range for its planes using a normal distribution of weights for adult passengers with a mean of 150 pounds and a standard deviation of 20 pounds. a. What is the probability that the mean weight of a group of 100 passengers will lie between 151 and 163 pounds? b. What is the probability that the mean weight of a group of 100 passengers is greater than 170 pounds? c. What is the probability that the mean weight of a group of 100 passengers is less than 140 pounds? d. What would be the weight mean of a group of 100 passengers if it capacity of the plane is in the top 10% of the airline?

Explanation / Answer

SolutionA:

mean=150

sd=20

n=100

P(151<X<163)

z=x-mean/sd/sqrt(n)

=P(151-150/20/sqrt(100)<z<163-150/20/sqrt(100)

=P(0.5<z<6.5)

=0.3085

ANSWER:0.3085

SOLUTIONB:

P(X>170)

z=170-150/20/sqrt(100)

=10

P(Z.>10)

=1-P(Z<10)

=1-1

=0

ANSWER:0

SOLUTIONC:

P(X<140)

Z=140-150/20/SQRT(100)

=-5

P(Z<-5)

=1-P(Z<5)

=1-1

=0

  

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