What is the likelihood of finding a price between $3.71 and $3.85 for a gallon of gasoline from a normally distributed population of gas prices? Assume μ = $3.78 and σ = $0.05.
A)0.4974
B)0.9948
C)0.8385
D)0.2487

Question

Quizplus · Accepted Answer

We need to find the probability of the gas price falling between $3.71 and $3.85. 
Using the z-score formula, we get:
z1 = (3.71 - 3.78) / 0.05 = -1.4
z2 = (3.85 - 3.78) / 0.05 = 1.4
Using a standard normal table or calculator, the probability of Z falling between -1.4 and 1.4 is 0.8385 or 83.85%. Therefore, the likelihood of finding a price between $3.71 and $3.85 is 0.8385 or 83.85%. The closest option is C.

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