The table to the right indicates the average price and stand

The table to the right indicates the average price and standard deviation in Anaheim for regular gasoline last month. The random sample generated the information below. Determine the lower boundary of the interval that contains 97% of the gasoline prices per gallon in Anaheim.

# of gas stations used in sample = 34

Average price of sample stations = $3.46/gal

µ = $ 3.57 / gal.

= $ 0.17 / gal.

Solution

CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=3.57
Standard deviation( sd )=0.19
Sample Size(n)=34
Confidence Interval = [ 3.57 ± Z a/2 ( 0.19/ Sqrt ( 34) ) ]
= [ 3.57 - 2.17 * (0.033) , 3.57 + 2.17 * (0.033) ]
= [ 3.499,3.641 ]

ower boundary of the interval = 3.50