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

George Ramirez · Accepted Answer

Final Answer : A, Explanation :   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 = X − μ σ z = \frac{X - \mu}{\sigma} z = σ X − μ ​  , where   X X X   is the value of interest ($3.85),   μ \mu μ   is the mean ($3.78), and   σ \sigma σ   is the standard deviation ($0.05). Plugging in the values, we get   z = 3.85 − 3.78 0.05 = 1.4 z = \frac{3.85 - 3.78}{0.05} = 1.4 z = 0.05 3.85 − 3.78 ​ = 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 1 - 0.9192 = 0.0808 1 − 0.9192 = 0.0808  , indicating a likelihood of 0.0808 or 8.08%.

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

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Learning Objectives

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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) 0.0808B) 0.4192C) 0.3508D) 0.1492

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Learning Objectives

Learning Objectives

Related questions

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