What is the likelihood of finding a price of $3.85 or more for a gallon of gasoline from a normally distributed population of gas prices? Assume μ = $3.78 and σ = $0.05.
A)0.0808
B)0.4192
C)0.3508
D)0.1492

Question

Quizplus · Accepted Answer

To find the likelihood of finding a price of $3.85 or more, we calculate the z-score and then look up the corresponding probability in a standard normal distribution table. The z-score is calculated as $z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest ($3.85), $\mu$ is the mean ($3.78), and $\sigma$ is the standard deviation ($0.05). Plugging in the values, we get $z = \frac{3.85 - 3.78}{0.05} = 1.4$. Looking up the z-score of 1.4 in a standard normal distribution table gives us the area to the left of the z-score, which is approximately 0.9192. To find the probability of getting a value of $3.85 or more, we subtract this from 1 (since the total area under the curve is 1), resulting in $1 - 0.9192 = 0.0808$, indicating a likelihood of 0.0808 or 8.08%.

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