Question

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.

Answer 1

The appropriate response is "0.9476".

Explanation:

The given values are:

Standard deviation,

`\sigma=1150`

Randomly selected railroad-car shipments,

n = 500

As we know,

⇒
`\sigma \bar{x}=(\sigma)/(√(n) )`

On substituting the values, we get

⇒
`=(1150)/(√(500) )`

then,

⇒
`=P(-1.94<Z<1.94)`

⇒
`=P(Z<1.94)-P(Z < -1.94)`

On using the table of P, we get

⇒
`=0.9738 - 0.0262`

⇒
`=0.9476`