Q: A student flips a coin $$5$$ times. What is the probability that exactly $$2$$ heads are observed?

$$P = \binom{5}{2} (0.5)^2$ (0.5)^3$ = 10 \times 0.25 \times 0.125 = 0.3125$$

Q: A home has $$1400$$ square feet and the regression equation for price is $$y = 50 + 0.1x$$, where $$y is $$the price in thousands of dollars and $$x is $$the square footage. What is the predicted price of the home?

$$y = 50 + 0.1 \times 1400 = 50 + 140 = 190$$ thousand dollars

Q: If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

$$P(A \cap B) = P(A) \times P(B) = 0.3 \times 0.5 = 0.15$$

Question 1

Suppose the birth weights of full-term babies are normally distributed with mean $$\mu = 3300$$ grams and standard deviation $$\sigma = 510$$ grams. What is the probability that a randomly selected baby weighs more than $$4230$$ grams?

Accepted Answer

$$P(X \u003e 4230) = 0.0228$$

Question 2

A researcher wants to test if a data set comes from a normal population. The sample size is $$n = 10$$ and the computed test statistic is $$0.945. $$The critical value from the table is $$0.879. $$What is the correct conclusion?

Accepted Answer

The test statistic $$0.945$$ exceeds the critical value $$0.879$$, so it is reasonable to conclude the data come from a normal population.

Question 3

A probability experiment is conducted with the given parameters: $$n = 6$$, $$p = 0.4$$, $$q = 0.6. $$What is the probability of exactly $$3$$ successes?

Accepted Answer

$$P(X = 3) = \binom{6}{3} (0.4)^3$ (0.6)^3$

Question 4

A survey of $$400$$ randomly selected high school students determined that $$200$$ play organized sports. What is the probability that a randomly selected student plays organized sports?

Accepted Answer

$$P = \frac{200}{400} = 0.5$$

Question 5

Suppose the mean number of chocolate chips in a cookie is $$\mu = 1200$$ and the standard deviation is $$\sigma = 50. $$What is the probability that a randomly selected cookie contains between $$1150$$ and $$1250$$ chocolate chips?

Accepted Answer

$$P(1150 \u003c X \u003c 1250) \approx 0.9544$$

Question 6

A contingency table shows the following: $$275$$ Americans are 'less likely' to be 15-34 years old, $$324$$ are 'more likely', and $$101$$ are 'no opinion'. What is the probability that a randomly selected American is 'more likely' to be 15-34 years old?

Accepted Answer

$$P = \frac{324}{275 + 324 + 101} = \frac{324}{700} \approx 0.463$$

Question 7

If the mean commute time for a city is $$\mu = 25$$ minutes and the standard deviation is $$\sigma = 5$$ minutes, what is the probability that a randomly selected resident has a commute time between $$20$$ and $$30$$ minutes?

Accepted Answer

$$P(20 \u003c X \u003c 30) \approx 0.6826$$

Question 8

A random variable $$X$$ can take the values $$1, 2, 3, 4, 5. Is$$ $$X$$ discrete or continuous?

Accepted Answer

Discrete, because $$X$$ can only take specific, countable values.

Question 9

A student flips a coin $$5$$ times. What is the probability that exactly $$2$$ heads are observed?

Accepted Answer

$$P = \binom{5}{2} (0.5)^2$ (0.5)^3$ = 10 	imes 0.25 	imes 0.125 = 0.3125$$

Question 10

A scatterplot of data shows a strong positive linear relationship. What is the expected sign and approximate value of the correlation coefficient $$r$$?

Accepted Answer

$$r is $$positive and close to $$1$$

Question 11

A home has $$1400$$ square feet and the regression equation for price is $$y = 50 + 0.1x$$, where $$y is $$the price in thousands of dollars and $$x is $$the square footage. What is the predicted price of the home?

Accepted Answer

$$y = 50 + 0.1 	imes 1400 = 50 + 140 = 190$$ thousand dollars

Question 12

If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B) = 0.3 	imes 0.5 = 0.15$$

Question 13

According to the Empirical Rule, what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

Approximately $$95\%$$

Question 14

A probability experiment is conducted with $$n = 4$$ and $$p = 0.7. $$What is the expected number of successes?

Accepted Answer

$$E(X) = n 	imes p = 4 	imes 0.7 = 2.8$$

Question 15

A random sample of $$100$$ students finds that $$47\%$$ started smoking before turning $$18$$ years old. What is the expected number of students who started smoking before $$18 in a $$random sample of $$150$$ students?

Accepted Answer

$$0.47 	imes 150 = 70.5$$ students

Question 16

Which of the following is NOT a requirement for a binomial probability experiment?

Accepted Answer

The trials must have a variable number of possible outcomes.

Question 17

If $$X is a $$normal random variable with mean $$\mu = 0$$ and standard deviation $$\sigma = 1$$, compute the probability $$P(-1 \u003c X \u003c 1).$$

Accepted Answer

$$P(-1 \u003c X \u003c 1) \approx 0.6826$$

Question 18

A student wants to know if the sum of the probabilities in a probability distribution must equal $$1. $$Which statement is correct?

Accepted Answer

Yes, because the sum of the probabilities is required to be $$1.$$

Comprehensive Study Notes: Core Concepts in Introductory Statistics

Study Guide - Practice Questions

Study Guide - Flashcards