Question

question 15 (1 point)

answer the question true or false.

the probability of success, \\(p\\), in a binomial experiment is a parameter, while the mean and standard deviation, \\(\mu\\) and \\(\sigma\\), are statistics.

true
false

question 16 (1 point)

solve the problem.

the average score of all golfers for a particular course has a mean of 69 and a standard deviation of 3. suppose 100 golfers played the course today. find the probability that the average score of the 100 golfers exceeded 70.

.3694
.4772
.0004
.0228

Explanation:

Define parameters and statistics

Using the Sample Statistics knowledge point, we distinguish between population characteristics and sample characteristics. A parameter is a numerical value that describes a population, whereas a statistic is a numerical value computed from a sample. In a binomial experiment, the probability of success \(p\) is a population parameter. The mean \(\mu\) and standard deviation \(\sigma\) of a probability distribution describe the entire population of outcomes, meaning they are also parameters, not statistics. Therefore, the statement in Question 15 is False.

Identify given values for Question 16

Using the Sampling Distribution of the Sample Mean knowledge point, we identify the population parameters and sample size:

• Population mean: \(\mu = 69\)
• Population standard deviation: \(\sigma = 3\)
• Sample size: \(n = 100\)
• Target value: \(\bar{X} > 70\)

Calculate the standard error

Using the Standard Error of the Mean knowledge point

$$ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{3}{\sqrt{100}} = \frac{3}{10} = 0.3 $$

Compute the Z-score

Using the Sampling Distribution of the Sample Mean knowledge point

$$ Z = \frac{\bar{X} - \mu}{\sigma_{\bar{x}}} = \frac{70 - 69}{0.3} = \frac{1}{0.3} \approx 3.33 $$

Find the probability

Using the Sampling Distribution of the Sample Mean knowledge point

$$ P(\bar{X} > 70) = P(Z > 3.33) = 1 - P(Z \le 3.33) \approx 1 - 0.9996 = 0.0004 $$

Answer:

Question 15

• True
• False (Correct answer)

Question 16

• .3694
• .4772
• .0004 (Correct answer)
• .0228