Answer: First option is correct.
Step-by-step explanation:
Since we have given that
Total area of square inches = 400
The area of the large circle = 314
Now, we need to find the probability that Trisha will not get any points with one randomly thrown dart that lands somewhere inside the square,
Let E be the event the Trisha will get points .
so,
As we know that
So, Probability that Trisha will not get any points with one randomly thrown dart that lands somewhere inside the square = 0.22
So, First option is correct.
Answer:
Step-by-step explanation:
y = x² + x - 3
x = - 3
y = ( - 3 )² + ( - 3 ) - 3 = 3
( - 3 , <em>3</em> )
x = 0 ⇒ y = - 3
( 0 , <em>- 3</em> )
x = 1
y = ( 1 )² + ( 1 ) - 3 = - 1
( 1 , <em>- 1 </em>)
<em>(b).</em> Coordinate x of the vertex of quadratic equation y = ax² + bx + c is
-
x = - = -
= - 0.5
y = ( - 0.5 )² + ( - 0.5 ) - 3 = - 3.25 = - 3
( - , - 3
)
Answer:
And if we solve for a we got
So the value of height that separates the bottom 10% of data from the top 90% is 64.08.
The graph attached illustrate the situation.
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".
Solution to the problem
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 10% of data from the top 90% is 64.08.
The graph attached illustrate the situation.
