Answer:
68.26% of regular grade gasoline sold between $3.33 and $3.53 per gallon
81.85% of regular grade gasoline sold between $3.33 and $3.63 per gallon
2.28% of regular grade gasoline sold for more than $3.63 per gallon
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
What percentage of regular grade gasoline sold between $3.33 and $3.53 per gallon?
This is the pvalue of Z when X = 3.53 subtracted by the pvalue of Z when X = 3.33. So
X = 3.53
has a pvalue of 0.8413
X = 3.33
has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
68.26% of regular grade gasoline sold between $3.33 and $3.53 per gallon
What percentage of regular grade gasoline sold between $3.33 and $3.63 per gallon?
This is the pvalue of Z when X = 3.53 subtracted by the pvalue of Z when X = 3.33. So
X = 3.63
has a pvalue of 0.9772
X = 3.33
has a pvalue of 0.1587
0.9772 - 0.1587 = 0.8185
81.85% of regular grade gasoline sold between $3.33 and $3.63 per gallon
What percentage of regular grade gasoline sold for more than $3.63 per gallon?
This is 1 subtracted by the pvalue of Z when X = 3.63. So
has a pvalue of 0.9772
1 - 0.9772 = 0.0228
2.28% of regular grade gasoline sold for more than $3.63 per gallon