An ethanol railroad tariff is a fee charge for shipments of ethanol on public railroads. The Agriculture Marketing Service publishes tariff rates for railroad-car shipments of ethanol in the Biofuel Transportation Database. Assuming that the standard deviation of such tariff rates is $1150, determine the probability that the mean tariff rate of 500 randomly selected railroad-car shipments of ethanol will be within $100 of the mean tariff rate of all railroad-car shipments of ethanol.

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Cricetus Cricetus · Answer 1 · 2021-03-30T17:29:28+02:00

Answer:

The appropriate response is "0.9476".

Step-by-step explanation:

The given values are:

Standard deviation,

[tex]\sigma=1150[/tex]

Randomly selected railroad-car shipments,

n = 500

As we know,

⇒ [tex]\sigma \bar{x}=\frac{\sigma}{\sqrt{n} }[/tex]

On substituting the values, we get

⇒ [tex]=\frac{1150}{\sqrt{500} }[/tex]

then,

⇒ [tex]=P(-1.94<Z<1.94)[/tex]

⇒ [tex]=P(Z<1.94)-P(Z < -1.94)[/tex]

On using the table of P, we get

⇒ [tex]=0.9738 - 0.0262[/tex]

⇒ [tex]=0.9476[/tex]