Using the normal distribution, there is a 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean 
and standard deviation 
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
For this problem, the parameters are given as follows:
The probability is the <u>p-value of Z when X = 16 subtracted by the p-value of Z when X = 15</u>, hence:
X = 16:
By the Central Limit Theorem
Z = 2.11
Z = 2.11 has a p-value of 0.9826.
X = 15:
Z = 0
Z = 0 has a p-value of 0.5.
0.9826 - 0.5 = 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.
More can be learned about the normal distribution at brainly.com/question/15181104
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To solve this problem, you have to divide the price by the number of gallons.
So 56.25/15 = 3.75
Therefore Genevieve payed $3.75 per gallon
The trapezoidal approximation will be the average of the left- and right-endpoint approximations.
Let's consider a simple example of estimating the value of a general definite integral,
Split up the interval
![[a,b]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D)
into
equal subintervals,
![[x_0,x_1]\cup[x_1,x_2]\cup\cdots\cup[x_{n-2},x_{n-1}]\cup[x_{n-1},x_n]](https://tex.z-dn.net/?f=%5Bx_0%2Cx_1%5D%5Ccup%5Bx_1%2Cx_2%5D%5Ccup%5Ccdots%5Ccup%5Bx_%7Bn-2%7D%2Cx_%7Bn-1%7D%5D%5Ccup%5Bx_%7Bn-1%7D%2Cx_n%5D)
where
and
. Each subinterval has measure (width)
.
Now denote the left- and right-endpoint approximations by
and
, respectively. The left-endpoint approximation consists of rectangles whose heights are determined by the left-endpoints of each subinterval. These are
. Meanwhile, the right-endpoint approximation involves rectangles with heights determined by the right endpoints,
.
So, you have
Now let
denote the trapezoidal approximation. The area of each trapezoidal subdivision is given by the product of each subinterval's width and the average of the heights given by the endpoints of each subinterval. That is,
Factoring out
and regrouping the terms, you have
which is equivalent to
and is the average of
and
.
So the trapezoidal approximation for your problem should be
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Step-by-step explanation:
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