Suppose that mean retail price per gallon of regular grade gasoline is 3.53 with a standard deviation of and that the retail price per gallon has a bell-shaped distribution. NOTE: Please use empirical rule approximations for this problem. a. What percentage of regular grade gasoline sells for between and per gallon (to decimal)

Incomplete question, but I gave a guide to solve using the Empirical Rule.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

It is also important to note that the normal distribution is symmetric. This means of the 68% of the measures are within 1 standard deviation of the mean, for example, 68/2 = 34% are between 1 standard deviation below the mean and the mean, and 34% are between the mean and 1 standard deviation above the mean.

In this question:

You take the mean and the standard deviation. Then you take both bounds that the percentage asks, and see how many standard deviations each are from the mean, and you then use the empirical rule to solve.

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: