Pregunta
- Mrs. Chauver has an interesting approach to assigning grades in her statistios elass. Of the 5 tests sfudents
take throughout the semester, Mrs, Chativet selects a fandomi sample of 3 , finds the average score of these tests,
and records this average as the student’s final grade. Joe’s test scores are as follows,
,
(a) List all 10 possible samples of size 3,
(b) Calculate the mean of each sample and display the sampling distribution of the sample mean using
a dotplot.
take throughout the semester, Mrs, Chativet selects a fandomi sample of 3 , finds the average score of these tests,
and records this average as the student’s final grade. Joe’s test scores are as follows,
(a) List all 10 possible samples of size 3,
(b) Calculate the mean of each sample and display the sampling distribution of the sample mean using
a dotplot.
Ask by Carrillo Collins. in the United States
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
There are 10 possible samples of size 3 from Joe’s test scores. The sample means are 85, 86, 87, 87, 88, 89, 90, 91, 92, and 93. The most frequent mean is 87, which appears twice.
Solución
Certainly! Let’s work through the problem step by step.
Problem 1
Mrs. Chauver assigns final grades by taking a random sample of 3 out of 5 test scores and averaging them. Joe’s test scores are as follows:
Part (a): List All 10 Possible Samples of Size 3
To determine all possible samples of size 3 from Joe’s 5 test scores, we can use combinations since the order of selection does not matter. The number of combinations is given by:
Here are all 10 possible samples:
- 93, 87, 96
- 93, 87, 78
- 93, 87, 90
- 93, 96, 78
- 93, 96, 90
- 93, 78, 90
- 87, 96, 78
- 87, 96, 90
- 87, 78, 90
- 96, 78, 90
Part (b): Calculate the Mean of Each Sample and Display the Sampling Distribution
Let’s calculate the mean for each of the 10 samples:
-
93, 87, 96
-
93, 87, 78
-
93, 87, 90
-
93, 96, 78
-
93, 96, 90
-
93, 78, 90
-
87, 96, 78
-
87, 96, 90
-
87, 78, 90
-
96, 78, 90
Sampling Distribution of the Sample Mean
The sampling distribution of the sample mean consists of all the sample means calculated above. Here’s a summary of the means and their frequencies:
Sample Mean | Frequency |
---|---|
85 | 1 |
86 | 1 |
87 | 2 |
88 | 1 |
89 | 1 |
90 | 1 |
91 | 1 |
92 | 1 |
93 | 1 |
Dotplot Representation
While I can’t provide a visual dotplot here, I can describe how you would create one:
- Draw a horizontal number line that spans from the lowest mean (85) to the highest mean (93).
- Plot each sample mean as a dot above its corresponding value on the number line.
- Stack dots vertically if multiple samples have the same mean.
For example:
85 | •
86 | •
87 | ••
88 | •
89 | •
90 | •
91 | •
92 | •
93 | •
This dotplot shows the distribution of Joe’s sample means, with 85 and 93 appearing once, 86 and 88-92 also appearing once each, and 87 appearing twice.
Interpretation
- Range of Sample Means: The means range from 85 to 93.
- Most Frequent Mean: 87 appears twice, making it the most frequent sample mean.
- Symmetry: The distribution is fairly symmetric around the center with a slight concentration towards the middle values.
This sampling distribution helps Mrs. Chauver understand the variability in Joe’s final grade based on different samples of his test scores.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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The Deep Dive
To tackle Mrs. Chauver’s grading method, let’s first list all possible samples of size 3 from Joe’s scores
. Here are the 10 possible combinations:
Now, let’s calculate the mean for each sample:
Here’s the sampling distribution of the sample means:
- Means:
Now, let’s visualize this with a simple dotplot where each mean from the samples is represented as a dot:
85: •
86: •
87: • •
88: •
89: •
90: •
91: •
92: •
93: •
Creating a dotplot like above allows us to quickly see the frequency of each mean value! This visual representation helps to understand how Joe’s grades might average out based on different testing combinations.

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