Question

QUESTION 7 5 points Save Answer Use the following to answer the next three exercises: The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. (1) The distribution to use for the average cost of gasoline for the 16 gas stations is: M&> N(4.59, ved B. ~ N(4.59, 0.1) C'~ N(4.59, 0:2) D.x(4.59, het 6 points Save Answer QUESTION 8 (2) What's the approximate probability that the average price for 16 gas stations is over $4.69? A. almost zero B. 0.1587 C.0.0943 D. unknown QUESTION 9 5 points Save Answer (3) If we randomly chose 30 gas stations, find the probability that the average price for 30 gas stations is less than $4.55. A. 0.0143 B.O C-0.6554 D. 0.9858 E. 0.3446

Answer 1

1)

Option c)

8)
Here, μ = 4.59, σ = 0.025 and x = 4.69. We need to compute P(X >= 4.69). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (4.69 - 4.59)/0.025 = 4

Therefore,
P(X >= 4.69) = P(z <= (4.69 - 4.59)/0.025)
= P(z >= 4)
= 1 - 1 = 0

9)

Here, μ = 4.59, σ = 0.018 and x = 4.55. We need to compute P(X <= 4.55). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (4.55 - 4.59)/0.018 = -2.19

Therefore,
P(X <= 4.55) = P(z <= (4.55 - 4.59)/0.018)
= P(z <= -2.19)
= 0.0143