Find the image of c under the translation described by the translation rule T<4,5> (C)
1 answer:
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Answer:
a) The probability of Jack scoring higher is 0.3446
b) They probability of them scoring above 350 is 0.2119
Step-by-step explanation:
Lets call X the random variable that determines Jill's bowling score and Y the random variable that determines jack's. We have
Note that we are considering the variance on the second entry, the square of the standard deviation.
If we have two independent Normal distributed random variables, then their sum is also normally distributed. If fact, we have this formulas:
for independent distributions ,
, and a real number r.
a) We define Z to be Y-X. We want to know the probability of Z being greater than 0. We have
So Z is a normal random variable with mean equal to -10 and vriance equal to 625. The standard deviation of Z is √625 = 25.
Lets work with the standarization of Z, which we will call W. = (Z+10)/25. W has Normal distribution with mean 0 and standard deviation 1. We have
P(Z > 0) = P( (Z+10)/25 > (0+10)/25) = P(W > 0.4)
To calculate that, we will use the <em>known </em>values of the cummulative distribution function Φ of the standard normal distribution. For a real number k, P(W < k) = Φ(k). You can find those values in the Pdf I appended below.
Since Φ is a cummulative distribution function, we have P(W > 0.4) = 1- Φ(0.4)
That value of Φ(0.4) can be obtained by looking at the table, it is 0.6554. Therefore P(W > 0.4) = 1-0.6554 = 0.3446
As a result, The probability of Jack's score being higher is 0.3446. As you may expect, since Jack is expected to score less that Jill, the probability of him scoring higher is lesser than 0.5.
b) Now we define Z to be X+Y Since X and Y are independent Normal variables with mean 160 and 170 respectively, then Z has mean 330. And the variance of Z is equal to the sum of the variances of X and Y, that is, 625. Hence Z is Normally distributed with mean 330 and standard deviation rqual to 25 (the square root of 625).
We want to know the probability of Z being greater that 350, for that we standarized Z. We call W the standarization. W is s standard normal distributed random variable, and it is obtained from Z by removing its mean 330 and dividing by its standard deviation 25.
P(Z > 350) = P((Z - 330)/25 > (350-330)/25) = P(W > 0.8) = 1-Φ(0.8)
The last equality comes from the fact that Φ is a cummulative distribution function. The value of Φ(0.8) by looking at the table is 0.7881, therefore P(X+Y > 350) = 1 - Φ(0.8) = 0.2119.
As you may expect, this probability is pretty low because the mean value of the sum of their combined scores is quite below 350.
I hope this works for you!
The transformations would map EFGH to is a reflection across line k followed by a translation down. Option (a) is correct.
Further explanation:
Given:
The compositions of transformations from EFGH to are as follows,
(a). A reflection across line k followed by a translation down.
(b). A translation down followed by a reflection across line k.
(c). A rotation about point G followed by a translation to the right.
(d). A translation to the right followed by a rotation about point G.
Explanation:
Translation can be defined as to move the function to a certain displacement. If the points of a line or any objects are moved in the same direction it is a translation.
Rotation is defined as a movement around its own axis. A circular movement is a rotation.
The transformations would map EFGH to is a reflection across line k followed by a translation down. Option (a) is correct.
Option (a) is correct.
Option (b) is not correct.
Option (c) is not correct.
Option (d) is not correct.
Learn more:
- Learn more about inverse of the functionhttps://brainly.com/question/1632445.
- Learn more about equation of circle brainly.com/question/1506955.
- Learn more about range and domain of the function brainly.com/question/3412497
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangles
Keywords: rotation, transformation, map, EFGH, composition, translation, triangle, rotation about point A, mapped, triangle pair, mapping, equal angles, sides, congruent, two triangles, common point.