Answer:
Step-by-step explanation:
Let and
. Now we evaluate the given function at
:
(1)
Which means that is less than the y-component of A. Therefore, the right answer is
.
If X and Y are random variables, the sum of all the conditional probabilities of X given a specific value of Y will always be:
1 answer:
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Answer:
g(x) = (x + 3)^2
Step-by-step explanation:
When a function is shifted to the left or right we can think of a change of units, like a new independent variable is used.
If we have a quadratic function
and the graph is shifted 3 units to the left, then we can think of a new unit u that is:
The vertix of this parabola, that happens for u=0, happens for x=-3, as the graph is shifted 3 units to the left.
Then, the relation between u and x is:
We can use this relation in the new graph and replace u as:
Answer:
a. 97.72% of the observations are less than 33
b. Approximately 977 observations are less than 33.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 25 and a standard deviation of 4.
This means that
a. Approximately what percentage of the observations are less than 33?
The proportion is the p-value of Z when X = 33. So
has a p-value of 0.9772
0.9772*100% = 97.72%
97.72% of the observations are less than 33.
b. Approximately how many observations are less than 33?
Out of 1000:
0.9772*1000 = 977.2
Approximately 977 observations are less than 33.