Using the normal distribution, it is found that there was a 0.9579 = 95.79% probability of a month having a PCE between $575 and $790.
<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.
The mean and the standard deviation are given, respectively, by:
.
The probability of a month having a PCE between $575 and $790 is the <u>p-value of Z when X = 790 subtracted by the p-value of Z when X = 575</u>, hence:
X = 790:
Z = 1.8
Z = 1.8 has a p-value of 0.9641.
X = 575:
Z = -2.5
Z = -2.5 has a p-value of 0.0062.
0.9641 - 0.0062 = 0.9579.
0.9579 = 95.79% probability of a month having a PCE between $575 and $790.
More can be learned about the normal distribution at brainly.com/question/4079902
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Answer:
Total volume in the two glasses is 740 mL.
Step-by-step explanation:
Given:
Ratio of the volume of soda in glass A to the volume of glass B = 8/3 : 7/2
Volume of soda in glass A = 320mL
To Find :
The total volume in the two glasses = ?
Solution:
Let the volume of soda in glass B be x
then
Substituting the values ,
x = 420
Now total volume of soda in the two glasses
=> volume of soda in glass A + volume of soda in glass B
=> 320 + 420
=>740mL
5.5 ( 8 - x ) + 44 = 104 - 3.5 ( 3x + 24 )
Distribute 5.5 through the parenthesis.
44 - 5.5x + 44 = 104 - 10.5x - 84
Add the numbers.
88 - 5.5x = 20 - 10.5x
Move variable to the left side and change its sign.
88 - 5.5x + 10.5x = 20
-5.5x + 10.5x = 20 -88
Collect like terms.
5x = 20 - 88
Calculate the sum or difference.
5x = - 68
Divide both sides by 5.
x = - 68 / 5
The vertex (minimum) of the quadratic ax² +bx +c is located at x=-b/(2a). This means the minimum value of f(x) will be found at x = -3/(2*1) = -1.5.
Since the vertex of the quadratic is less than 0, the maximum value of the quadratic will be found at x=2, the end of the interval farthest from the vertex.
On the given interval, ...
the absolute minimum value of f is f(-1.5) = ln(1.75) ≈ 0.559616
the absolute maximum value of f is f(2) = ln(14) ≈ 2.639057
