If the dresses are chosen at random a probability tree can be constructed showing the probabilities of the various combinations that are possible. It shows the total probability of choosing a black, then white, or a white, then black dress is 1/9.
Answer:
1, 2, 6
Step-by-step explanation:
The z score shows by how many standard deviations the raw score is above or below the mean. The z score is given by:
![z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \ \sigma=standard\ deviation](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5C%5C%5C%5Cwhere%5C%20x%3Draw%5C%20score%2C%5Cmu%3Dmean%2C%20%5C%20%5Csigma%3Dstandard%5C%20deviation)
Given that mean (μ) = 130 texts, standard deviation (σ) = 20 texts
1) For x < 90:
![z=\frac{x-\mu}{\sigma} \\\\z=\frac{90-130}{20} =-2](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5C%5C%5C%5Cz%3D%5Cfrac%7B90-130%7D%7B20%7D%20%3D-2)
From the normal distribution table, P(x < 90) = P(z < -2) = 0.0228 = 2.28%
Option 1 is correct
2) For x > 130:
![z=\frac{x-\mu}{\sigma} \\\\z=\frac{130-130}{20} =0](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5C%5C%5C%5Cz%3D%5Cfrac%7B130-130%7D%7B20%7D%20%3D0)
From the normal distribution table, P(x > 130) = P(z > 0) = 1 - P(z < 0) = 1 - 0.5 = 50%
Option 2 is correct
3) For x > 190:
![z=\frac{x-\mu}{\sigma} \\\\z=\frac{190-130}{20} =3](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5C%5C%5C%5Cz%3D%5Cfrac%7B190-130%7D%7B20%7D%20%3D3)
From the normal distribution table, P(x > 3) = P(z > 3) = 1 - P(z < 3) = 1 - 0.9987 = 0.0013 = 0.13%
Option 3 is incorrect
4) For x < 130:
![z=\frac{x-\mu}{\sigma} \\\\z=\frac{130-130}{20} =0](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5C%5C%5C%5Cz%3D%5Cfrac%7B130-130%7D%7B20%7D%20%3D0)
For x > 100:
![z=\frac{x-\mu}{\sigma} \\\\z=\frac{100-130}{20} =-1.5](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5C%5C%5C%5Cz%3D%5Cfrac%7B100-130%7D%7B20%7D%20%3D-1.5)
From the normal table, P(100 < x < 130) = P(-1.5 < z < 0) = P(z < 0) - P(z < 1.5) = 0.5 - 0.0668 = 0.9332 = 93.32%
Option 4 is incorrect
5) For x = 130:
![z=\frac{x-\mu}{\sigma} \\\\z=\frac{130-130}{20} =0](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5C%5C%5C%5Cz%3D%5Cfrac%7B130-130%7D%7B20%7D%20%3D0)
Option 5 is incorrect
6) For x = 130:
![z=\frac{x-\mu}{\sigma} \\\\z=\frac{160-130}{20} =1.5](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5C%5C%5C%5Cz%3D%5Cfrac%7B160-130%7D%7B20%7D%20%3D1.5)
Since 1.5 is between 1 and 2, option 6 is correct
The number of terms in the expression is 2
<u><em>Both the statement and its contrapositive are true. </em></u>A right angle will always be 90 degrees, so both are true.