Q: The board of examiners that administers the real estate broker’s examination in a certain state found that the scores in the exam are normally distributed with mean score of $$435$$ and standard deviation of $$72. $$What is the 80th percentile score in this exam?

$$z=0.84$$, so $$X=435+0.84\times72=495.48$$

Question 1

A recent survey found that 55% of college students live on campus, 60% have a campus meal program, and 33% do both. Living on campus and having a meal program are:

Accepted Answer

Dependent

Question 2

Suppose you record the total number of times you are stopped by a red light out of 3 traffic lights on your way to school. What is the sample space?

Accepted Answer

$$S = \{0,1,2,3\}$$

Question 3

Let $$X be a $$binomial random variable with $$n=10$$ and $$p=0.4$$, and let $$Y be a $$normal random variable with mean $$=4$$ and variance $$=24. $$Then:

Accepted Answer

$$P(X\u003c5) \approx P(Y\u003c5)$$

Question 4

Let $$X be a $$binomial random variable with $$n=1000$$ and $$p=0.4$$, and let $$Y be a $$normal random variable with mean $$=400$$ and variance $$=240. $$Then:

Accepted Answer

$$P(X\u003e199) \approx P(Y\u003e199.5)$$

Question 5

Let $$Y be a $$normal random variable with mean $$=10$$ and variance $$=4. $$Let $$Z be a $$normal random variable with mean $$=0$$ and variance $$=1. $$Which is correct?

Accepted Answer

$$P(Y\u003e12) = P(Z\u003e2)$$

Question 6

Let $$U be a $$uniform random variable with min $$=5$$ and max $$=10. $$What is $$P(U\u003e7)$$?

Accepted Answer

$$0.4$$

Question 7

If $$A$$ and $$B$$ are any two events, then $$P(A \cap B) = P(B|A) \cdot P(A). Is $$this statement true?

Accepted Answer

True

Question 8

If $$A$$ and $$B$$ are any two events such that $$P(A|B) = P(A)$$, then $$A$$ and $$B$$ are independent.

Accepted Answer

True

Question 9

The probability that a concert will be well-advertised is $$0.8$$, and the probability that it will be well-advertised and a great success is $$0.74. $$What is the probability that the concert will be a great success if it is well-advertised?

Accepted Answer

$$0.925$$

Question 10

Let $$X$$ and $$Y be $$two independent random variables with $$E(X)=4$$ and $$E(Y)=10. $$Define the random variable $$W as$$ $$W=3X-Y. $$Then $$E(W) is$$:

Accepted Answer

$$2$$

Question 11

Let $$X$$ and $$Y be $$two independent random variables. We know that $$Var(Y)=4. $$Define the random variable $$W as$$ $$W=3X-2Y. $$Then $$Var(W) is$$:

Accepted Answer

$$9Var(X)+4Var(Y)$$

Question 12

Let $$Z be a $$normal random variable with mean $$0$$ and variance $$1. $$Then, $$P(Z\u003e1.96) = P(Z\u003c-1.96). Is $$this statement true?

Accepted Answer

True

Question 13

Let $$X be a $$normal random variable with mean $$100$$ and variance $$4. $$Then, $$P(X\u003e100) = 50\%. Is $$this statement true?

Accepted Answer

True

Question 14

Data show that 20% of all patients who make an appointment at a primary-care clinic never show up. Suppose 5 patients make appointments. Let $$X be $$the number of patients who never show up. What is the probability that all 5 patients show up?

Accepted Answer

$$0.32768$$

Question 15

A school is organizing a talent show, and there are 12 students who have signed up to perform. The students include 5 singers, 3 dancers, and 4 actors. How many different groups of 5 students can the organizer choose?

Accepted Answer

$$792$$

Question 16

The board of examiners that administers the real estate broker’s examination in a certain state found that the scores in the exam are normally distributed with mean score of $$435$$ and standard deviation of $$72. $$What is the 80th percentile score in this exam?

Accepted Answer

$$z=0.84$$, so $$X=435+0.84	imes72=495.48$$

Question 17

According to the data, 6% of human population has blood type O-negative. Suppose we have a random sample of size $$n=500$$ from this population. Let $$X be $$the number of human population with blood type O-negative. What is the mean and variance of $$X$$?

Accepted Answer

Mean $$=30$$, Variance $$=28.2$$

Question 18

A cybersecurity analyst monitors network alerts to detect real cyberattacks among false alarms. On any given alert, the analyst is focused 70% of the time. When focused, the analyst correctly identifies a true attack 90% of the time. What is the probability that the analyst will correctly identify a true attack?

Accepted Answer

$$0.63$$

Statistics Study Guide: Probability, Random Variables, Distributions, and Combinatorics

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