A survey of the 12th grade students at Gaffigan High School found that 84% of the seniors have their driver’s licenses, 16% of s

Answer:

Clarified below.

Detailed explanation:

A population refers to the entire group of data available for analysis, from which a smaller set is selected for closer scrutiny. This population can include individuals, articles, experiments, or measurements. Hence, a population represents a compilation of data pertaining to subjects that are linked by a shared feature.

A sample is a smaller, manageable portion derived from a larger group. It embodies the traits of a broader population. Samples are utilized in statistical tests when the overall population size is too vast to feasibly include all members in the analysis.

A parameter plays a significant role in statistical analysis. It refers to the attributes that characterize a specific population. Examples include population mean, population standard deviation, population proportion, etc.

When forming a statistical inference about the population being examined, the parameter value remains unknown because collecting data from every single individual in the population is unfeasible. Therefore, a sample is drawn from the population to draw conclusions about the parameter.

A statistic is the calculated value derived from this sample's characteristics. For instance, this includes sample mean, sample standard deviation, sample proportion, etc.

The matched pairs are represented as follows:

Population: 2. All Toyota Camry (2020 US) model vehicles.

Sample: 4. A selection of 117 Toyota Camry (2020 US) vehicles that were picked.

Parameter: 7. The mean mileage of all Toyota Camry (2020 US) model vehicles.

Statistics: 6. The city mileage averaged for the 117 sampled Toyota Camry (2020 US) cars, which is 27.8 mpg.

A. Mean and standard deviation.

The sampling distribution’s mean closely matches the population mean. Since the population mean is 174.5, the sampling distribution’s mean equals this value.

The standard deviation of the sampling distribution is:

            σₓ̄ = σ / √n

Plugging in values:

            σₓ̄ = 6.9 / √25 = 1.38

b. Calculate z-scores for both values:
         
      z = (value - mean) / standard deviation

For 172.5:
     z = (172.5 - 174.5) / 1.38 = -1.49
Corresponding probability ≈ 0.068

For 175.8:
   z = (175.8 - 174.5) / 1.38 = 0.94
Corresponding probability ≈ 0.83

The difference between these probabilities is 0.762.

Approximately 0.762 × 200 = 152 sample means lie between 172.5 and 175.8.

c. Z-score for 172 cm:

    z = (172 - 174.5) / 1.38 = -1.81
Probability ≈ 0.03

Hence, samples with means below 172 cm equal 0.03 × 200 = 6.

Answer: 56/81

Step-by-step explanation:

refer to the attached document

An equivalent decimal represents the same quantity as another decimal; here, the 0 does not contribute any value.