Answer:
a)
And we can find this probability with the normal standard table or excel:
b)
And we can find this probability with the normal standard table or excel:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the amount of gas of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with the normal standard table or excel:
Part b
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with the normal standard table or excel:
Answer: 7/8
Step-by-step explanation:
To find the equivalent expression of a fraction, we can either multiply numerator and denominator by same variable or same number, or we can divide both numerator and denominator by same number or same variable .
So if we multiply both numerator and denominator by 2, we will get
Answer: Transitive Postulate of Inequality (last option)
Explanation:
Let's say we have a vacation where we go from City A, to City B, then to City C. We can use the notation . If all we cared about was the first and last cities, then we basically say
taking a shortcut so to speak.
This analogy is useful to describe the transitive property.
The equality version is where if we had a = b and b = c, then a = c.
The inequality version is where if we had a < b and b < c, then a < c. In this case, c = 2.
In a sense, its like linking together metal chains. A leads to B which leads to C. So we can just jump from A to C.
It might help to draw out a number line and pick values for a and b like a = 0 and b = 1. That way you can see how a < b, b < c and a < c all tie together.