Question 1

From a group of 5 students (A, B, C, D, E), three are chosen at random. What is the probability that both A and E are chosen?

Accepted Answer

$$\frac{3}{10}$$

Question 2

In a survey, students were asked how many siblings they had. The frequency distribution is: 0 siblings (35), 1 sibling (95), 2 siblings (48), 3 siblings (24), 4 siblings (18). What is the probability that a randomly selected student has fewer than two siblings?

Accepted Answer

$$\frac{130}{220}$$

Question 3

A survey of 100 MSU students found that 65 supported the governor’s policies (43 male), and 35 did not (21 male). What is the probability that a randomly chosen student was female?

Accepted Answer

$$0.36$$

Question 4

Given the probability distribution for a discrete random variable $$X$$: $$P(X=2)=0.15$$, $$P(X=3)=0.3$$, $$P(X=4)=0.3$$, $$P(X=5)=0.25. $$What is the expected value $$E(X)$$?

Accepted Answer

$$3.65$$

Question 5

Given the same probability distribution as above, what is the standard deviation of $$X$$?

Accepted Answer

$$1.01$$

Question 6

In a survey, 69% of students use Yahoo as their primary search engine. If 10 students are chosen at random, what is the expected number of students who use Yahoo?

Accepted Answer

$$6.9$$

Question 7

Using the binomial distribution, what is the probability that exactly 3 out of 10 randomly chosen students use Yahoo, given that the probability of using Yahoo is 0.69?

Accepted Answer

$$0.0108$$

Question 8

Scores on a standardized test are normally distributed with mean $$\mu=24$$ and standard deviation $$\sigma=3.5. $$What percent of students score 25 or higher?

Accepted Answer

$$38.59\%$$

Question 9

For the same test, what is the probability that a student scores between 21 and 26?

Accepted Answer

$$0.5208$$

Question 10

According to the Empirical Rule, 99.74% of scores on a normal distribution fall between which two values for a test with mean $$24$$ and standard deviation $$3.5$$?

Accepted Answer

$$13.5$$ and $$34.5$$

Question 11

If a student scored at the 83rd percentile on the standardized test (mean $$24$$, standard deviation $$3.5$$), what was their test score (rounded to the nearest integer)?

Accepted Answer

$$27$$

Question 12

Using the standard normal table, what is $$P(Z \u003c 2.3)$$?

Accepted Answer

$$0.9893$$

Question 13

What is the value of $$z$$ such that $$P(Z \u003c z) = 0.1075$$?

Accepted Answer

$$-1.24$$

Question 14

In a binomial experiment with $$n=10$$ and $$p=0.69$$, what is the standard deviation?

Accepted Answer

$$1.46$$

Question 15

Given the probability distribution $$P(X=2)=0.15$$, $$P(X=3)=0.3$$, $$P(X=4)=0.3$$, $$P(X=5)=0.25$$, what is $$P(3 \leq X \u003c 5)$$?

Accepted Answer

$$0.6$$

Question 16

In a survey of 100 MSU students, what is the probability that a randomly chosen student is either male or did not support the governor’s policies?

Accepted Answer

$$0.78$$

Question 17

If $$Z is a $$standard normal random variable, what is $$P(Z \u003e 1.76)$$?

Accepted Answer

$$0.0392$$

Question 18

For a binomial experiment with $$n=10$$ and $$p=0.69$$, what is the probability that fewer than 2 students use Yahoo?

Accepted Answer

$$0.0002$$

Question 19

What is the value of $$z_{0.02}$$, the $$z-$$score such that the area to the right is $$0.02$$?

Accepted Answer

$$2.05$$

Question 20

From a group of 5 students (A, B, C, D, E), three are chosen at random. What is the probability that D is not chosen?

Accepted Answer

$$0.4$$

Step-by-Step Guidance for Introductory Statistics Practice Questions

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