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# ASSESSMENT Read each item carefully. Write the letter of the best answer for each test item before the number. 1. Which of the following statement describe a continuous random variable? A. The number of students present in a Class Temperance. B. The average distance travelled by a tricycle in a month. C. The number of motorcycles owned by a randomly selected household. D. The number of girls taller than 5 feet in a random sample of 6 girls. 2. Which of the following is an example of discrete variable? A. Distance travelled between cars. C. Number of blue marbles in the box. B. Height of the students in a section. D. Weight of potatoes in the basket. 3. You decided to conduct a survey of families with two children. You are interested incounting the number of girls (out of 2 children) in each family. Is this a random variable? A. Yes, it is a random variable. C. Maybe. B. No, it is not a random variable. D. Cannot be determined. 4. Suppose you tossed three coins. What are the sample spaces for the experiment above? A. HHH, TTT C. TTT, HHH, TTH, THT, HTH B. TTT, HHH, HHT, THT, HTH D. TTT, TTH, THT, HTT, HHT, HTH, THH, HHH 5. Suppose three laptops are tested. Let D represent the defective laptop and N for the non-defective laptop. How many possible outcomes will occur from the experiment? A. 3 B. 4 C. 8 D. 9 6. Based on number 5, if we let $X$ be the random variable representing the number of non-defective laptops. What are the possible values of the random variable? A. 0,1 B. $0,1,2$ C. 1, 2, 3 D. $0,1,2,3$ 7. Which probability distribution represents the given problem on number 6? A. B. | $x$ | 0 | 1 | 2 | | :-- | :-- | :-- | :-- | | $P(x)$ | $1 / 2$ | $1 / 2$ | $1 / 4$ | | $x$ | 0 | 1 | 2 | | :-- | :-- | :-- | :-- | | $P(x)$ | $1 / 2$ | $3 / 8$ | $3 / 8$ | C. D. | $x$ | 0 | 1 | 2 | | :-- | :-- | :-- | :-- | | $P(x)$ | $1 / 4$ | $1 / 2$ | $1 / 4$ | | $x$ | 0 | 1 | 2 | 3 | | :-- | :-- | :-- | :-- | :-- | | $P(x)$ | $1 / 8$ | $1 / 8$ | $35 / 8$ | $1 / 8$ | 8. The given table represents a probability distribution. What is $P(x) \mathrm{i}^{2} x= 1 + 4$ ? | $x$ | 4 | 8 | 16 | 16 | | :--: | :--: | :--: | :--: | :--: | | $P(x)$ | 1 | 2 | 3 | 3 |

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Answer

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Step 1:
: Identify the correct answer for question 1.

The correct answer is D. The number of girls taller than 5 feet in a random sample of 6 girls. This is because the height of individuals is continuous, but the condition of being a girl taller than 5 feet creates a discrete set of possibilities.

Step 2:
: Identify the correct answer for question 2.

The correct answer is C. Number of blue marbles in the box. This is because the number of marbles is discrete, as you can either have a marble or not have a marble (i.e., whole numbers only).

Step 3:
: Identify the correct answer for question 3.

The correct answer is A. Yes, it is a random variable. The number of girls in a family with two children can be either 0, 1, or 2, making it a random variable.

Step 4:
: Identify the correct answer for question 4.

The correct answer is D. TTT, TTH, THT, HTT, HHT, HTH, THH, HHH. This represents all possible outcomes when tossing three coins.

Step 5:
: Identify the correct answer for question 5.

The correct answer is C. 9. There are 3 possibilities for each laptop (defective or non-defective), leading to 2^3 = 9 possible outcomes.

Step 6:
: Identify the correct answer for question 6.

Since $X$ represents the number of non-defective laptops, its possible values range from 0 (all are defective) to 2 (none or one are defective).

The correct answer is B. 0, 1, 2.

Step 7:
: Identify the correct answer for question 7.

| $P(x)$ | $1 / 2$ | $3 / 8$ | $3 / 8$ |

The correct answer is B. | :-- | :-- | :-- | :-- | This table represents the probability distribution for the number of non-defective laptops in a sample of 3.

Step 8:
: Calculate $P(x) i^{2} x= 1 + 1$ for question 8.

Given the table: | :--: | :--: | :--: | :--: | :--: | We have: \begin{align*} P(x) i^{2} x= 1 + 4 &= P(1) + P(4) \ &= 2 + 1 \ &= 3 \end{align*}

Final Answer

1. D 2. C 3. A 4. D 5. C 6. B 7. Table B 8. $P(x) i^{2} x= 1 + 4 = 1$

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Answer

Full Solution Locked

Step 1:
: Identify the correct answer for question 1.

Step 2:
: Identify the correct answer for question 2.

Step 3:
: Identify the correct answer for question 3.

Step 4:
: Identify the correct answer for question 4.

Step 5:
: Identify the correct answer for question 5.

Step 6:
: Identify the correct answer for question 6.

Step 7:
: Identify the correct answer for question 7.

Step 8:
: Calculate $P(x) i^{2} x= 1 + 1$ for question 8.

Final Answer

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Full Solution Locked

Step 1:: Identify the correct answer for question 1.

Step 2:: Identify the correct answer for question 2.

Step 3:: Identify the correct answer for question 3.

Step 4:: Identify the correct answer for question 4.

Step 5:: Identify the correct answer for question 5.

Step 6:: Identify the correct answer for question 6.

Step 7:: Identify the correct answer for question 7.

Step 8:: Calculate $P(x) i^{2} x= 1 + 1$ for question 8.

Final Answer

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Answer

Step 1:
: Identify the correct answer for question 1.

Step 2:
: Identify the correct answer for question 2.

Step 3:
: Identify the correct answer for question 3.

Step 4:
: Identify the correct answer for question 4.

Step 5:
: Identify the correct answer for question 5.

Step 6:
: Identify the correct answer for question 6.

Step 7:
: Identify the correct answer for question 7.

Step 8:
: Calculate $P(x) i^{2} x= 1 + 1$ for question 8.