What is the value for x
2 answers:
Because this is a right angle triangle, we can use the Pythagorean theorem to find the missing leg.
The Pythagorean theorem is this:
The Pythagorean theorem tells us if you square both the legs then add them up together, you will get the length of the hypotenuse squared.
We know one leg is 24 and the hypotenuse is 26. Plug them into the equation.
24^2 + b^2 = 26^2
Solve for b.
24^2 + b^2 = 26^2
576 + b^2 = 26^2
576 + b^2 = 676
b^2 = 100
Take the square root of both sides.
b = 10
So, the other leg of the triangle is 10 units long.
The Pythagorean theorem is this:
The Pythagorean theorem tells us if you square both the legs then add them up together, you will get the length of the hypotenuse squared.
We know one leg is 24 and the hypotenuse is 26. Plug them into the equation.
24^2 + b^2 = 26^2
Solve for b.
24^2 + b^2 = 26^2
576 + b^2 = 26^2
576 + b^2 = 676
b^2 = 100
Take the square root of both sides.
b = 10
So, the other leg of the triangle is 10 units long.
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Answer:
1) FALSE
2) FALSE
3) TRUE
4) TRUE
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 1
The mean and standard deviation of a normally distributed random variable which has been standardized are one and zero, respectively.
The mean and the deviation for the normal standard distribution are:
So then that's FALSE.
Part 2
Using the standard normal curve, the z−score representing the 10th percentile is 1.28.
We are looking for a value a, that satisfy this:
(a)
(b)
We can find a 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<-1.28)=0.10 and P(Z>-1.28)=0.90
So that's FALSE.
Part 3
Let z1 be a z−score that is unknown but identifiable by position and area. If the symmetrical area between −z1 and +z1 is 0.9544, the value of z1 is 2.0
If we find this probability:
So on this case we can approximate to 0.9544. And that's TRUE.
Part 4
Using the standard normal curve, the z−score representing the 75th percentile is 0.67.
We are looking for a value a, that satisfy this:
(a)
(b)
We can find a z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.67. On this case P(Z<0.67)=0.75 and P(Z>0.67)=0.25
So that's TRUE.