Question

1. In the gasoline mileage problem, suppose that the population of all mileages is normally distributed with mean μ = 31.5 and standard deviation ?= .8. Calculate the three intervals.

2. In the gasoline mileage problem the population of all mileages is normally distributed with meanμ = 31.5 and standard deviation u = .8. Calculate the z value corresponding to the mileage 29.9, 33.1, and 31 mpg.

Answer 1

1)

first interval

µ±σ = 31.5±0.8 = (30.7,32.3)

second interval

µ±2σ = (31.5±2*0.8) = (29.9,33.1)

third interval

µ±3σ = (31.5±3*0.6) = (29.1,33.9)

2)

29.9

Z =(X - µ ) / σ = (   29.9   -   31.5   ) /    0.8
Z =    -2.000              
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33.1

Z =(X - µ ) / σ = (   33.1   -   31.5   ) /    0.8
Z =    2.000              
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31

Z =(X - µ ) / σ = (   31   -   31.5   ) /    0.8
Z =    -0.625