Find the probability and interpret the results. If convenient, use technology to
ID: 3385691 • Letter: F
Question
Find the probability and interpret the results. If convenient, use technology to find the probability. During a certain week the mean price of gasoline was $2.709 per gallon. A random sample of 35 gas stations is drawn from this population. What is the probability that the mean price for the sample was between $2.699 and $2.724 that week? Assume sigma = $0.043. The probability that the sample mean was between $2.699 and $2.724 is . A. About 10% of the population of 35 gas stations that week will have a mean price between $2.699 and $2.724. B. About 90% of the sample of 35 gas stations that week will have a mean price between $2.699 and $2.724. C. About 10% of the sample of 35 gas stations that week will have a mean price between $2.699 and $2.724. D. About 90% of the population of 35 gas stations that week will have a mean price between $2.699 and $2.724.Explanation / Answer
a)
We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as
x1 = lower bound = 2.699
x2 = upper bound = 2.724
u = mean = 2.709
n = sample size = 35
s = standard deviation = 0.043
Thus, the two z scores are
z1 = lower z score = (x1 - u) * sqrt(n) / s = -1.375832508
z2 = upper z score = (x2 - u) * sqrt(n) / s = 2.063748762
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.084436747
P(z < z2) = 0.980479228
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.8960 [ANSWER]
******************
b)
OPTION B: About 90% of samples of 35 gas stations that week will have a mean pricebetween 2.699 and 2.724. [ANSWER, B]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.