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alisha [4.7K]
3 years ago
13

In a sample of 700 gas​ stations, the mean price for regular gasoline at the pump was $2.894 per gallon and the standard deviati

on was ​$0.009 per gallon. A random sample of size 55 is drawn from this population. What is the probability that the mean price per gallon is less than ​$​2.892?
Mathematics
1 answer:
frez [133]3 years ago
3 0

Answer:

P(x < 2.892) = 4.36\%

Step-by-step explanation:

Given

N = 700 --- Population

\mu = 2.894 -- Mean

\sigma = 0.009 --- Standard deviation

n = 55 -- Sample

Required: P(x < 2.892)

This question will be solved using the finite correction factor

First, calculated the z score

z = \frac{x - \mu}{\sqrt{\frac{N -n}{N -1}} * \frac{\sigma}{\sqrt n}}

z = \frac{2.892 - 2.894}{\sqrt{\frac{700 -55}{700 -1}} * \frac{0.009}{\sqrt {55}}}

z = \frac{-0.002}{\sqrt{\frac{645}{699}} * \frac{0.009}{7.42}}

z = \frac{-0.002}{\sqrt{0.92} * \frac{0.009}{7.42}}

z = \frac{-0.002}{0.95917 * 0.0012129}

z = -1.71

So:

P(x < 2.892) = P(z < -1.71)

Using z table

P(x < 2.892) = 0.043633

P(x < 2.892) = 4.36\%

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