Tanker trucks are designed to carry huge quantities of gasol

Tanker trucks are designed to carry huge quantities of gasoline from refineries to filling stations. A factory that manufactures the tank of the trucks claims to manufacture tanks with a capacity of 8550 gallons of gasoline. The actual capacity of the tanks is normally distributed with mean = 8544 gallons and standard deviation = 12 gallons. Use this information to answer questions 7 through 10.

Solution

(7) Z-score = (X-mean)/s

=(8550-8544)/12

=0.5

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(8) The probability is

P(X<8550) = P(Z<(8550-8544)/12)

=P(Z<0.5)

=0.6915 (from standard normal table)

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(9) Z-score= (xbar-mean)/(s/vn)

=(8550-8544)/(12/sqrt(20))

=2.24

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(10) P(xbar> 8540)

=P(Z>(8540-8544)/(12/sqrt(50)))

=P(Z>-2.36)

=0.9909 (from standard normal table)