Question 1

A university reports that 38% of its students prefer online textbooks. A professor randomly surveys 120 students in her class and finds that 54 of them prefer online textbooks. What is the sample proportion, and what is its symbol?

Accepted Answer

The sample proportion is $$\hat{p} = \frac{54}{120} = 0.45$$

Question 2

A bottled water company claims that the true average fill amount is 16 ounces. A quality control manager selects 25 bottles and finds the average fill amount is 15.6 ounces with a standard deviation of 0.8 ounces. What is the sample mean, and what is its symbol?

Accepted Answer

The sample mean is $$\bar{x} = 15.6$$

Question 3

Suppose $$X is a $$continuous random variable. If $$P(X  8)$$?

Accepted Answer

$$P(X \u003e 8) = 0.07$$

Question 4

For $$X \sim N(11, 2)$$, what is the variance of this distribution?

Accepted Answer

Variance is $$2^2 = 4$

Question 5

The graph below shows the distribution of test scores taken by College Algebra students. The maximum possible score on the test was 140. What is the mean and standard deviation of this distribution if the mean is at 75 and the standard deviation is 15?

Accepted Answer

Mean = 75, Standard deviation = 15

Question 6

A normal distribution is described as $$X \sim N(\mu, \sigma). If $$the mean is 72 and the variance is 36, what is the standard deviation?

Accepted Answer

$$\sigma = 6$$

Question 7

Using the Empirical Rule, what percentage of scores are between 66 and 78 for a normal distribution with mean 72 and standard deviation 6?

Accepted Answer

Approximately 68%

Question 8

For $$Z \sim N(0,1)$$, what does this notation mean?

Accepted Answer

The random variable $$Z$$ follows a normal distribution with mean 0 and standard deviation 1.

Question 9

Which statement best describes a $$z-$$score?

Accepted Answer

The number of standard deviations a value is from the mean

Question 10

A student completes an online statistics activity in 40 minutes. The mean completion time is 50 minutes with a standard deviation of 10 minutes. What is the standardized score (z-score) for this student?

Accepted Answer

$$z = \frac{40 - 50}{10} = -1$$

Question 11

The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal under certain conditions. Which of the following is a necessary condition for the Central Limit Theorem to be used?

Accepted Answer

The population from which we are sampling must be normally distributed OR the sample size must be large (e.g., at least 30).

Question 12

A researcher increases the sample size from 25 participants to 100 participants while studying blood pressure. What happens to the standard deviation of the sampling distribution?

Accepted Answer

It decreases.

Question 13

A fair coin is flipped many times. After the first 10 flips, the proportion of heads is 0.70. According to the Law of Large Numbers, what will happen as the number of flips continues to increase?

Accepted Answer

The proportion of heads will eventually move closer to 0.50 as more flips are performed.

Question 14

A population of values has a normal distribution $$X \sim N(88, 28). $$You intend to draw a random sample of size 15. What is the probability that a single randomly selected value is greater than 90?

Accepted Answer

$$P(X \u003e 90) = P\left(Z \u003e \frac{90-88}{28}\right) = P(Z \u003e 0.071) \approx 0.472$$

Question 15

A large candy company claims that 27% of its candies are red. A random sample of 120 candies is selected. Which condition must be checked to use the normal approximation to the binomial distribution?

Accepted Answer

$$np$$ and $$n(1-p)$$ are both at least 5.

Introductory Statistics Exam 2 Review – Step-by-Step Study Guidance

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