Problem: As a Physical Education teacher of Hermosa National Hich School Senior High School, Ma'am Mary Ann wants to compute for the Body Mass Index of few students as part of her research. As a start, the table below shows the heights of five students in meters. Supposed samples of size 2 are taken from this population of five students, complete the given table and answer the following tasks. Construct the desired tables needed for your solutions and answers.
Problem: As a Physical Education teacher of Hermosa National Hich School Senior High School, Ma'am Mary Ann wants to compute for the Body Mass Index of few students as part of her research. As a start, the table below shows the heights of five students in meters. Supposed samples of size 2 are taken from this population of five students, complete the given table and answer the following tasks. Construct the desired tables needed for your solutions and answers.
A First Course in Probability (10th Edition)
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Transcribed Image Text:Direction: Solve the given real - life problem below. Show the complete
solution for the following tasks.
Problem: As a Physical Education teacher of Hermosa National High
School Senior High School, Ma'am Mary Ann wants to compute for the
Body Mass Index of few students as part of her research. As a start, the
table below shows the heights of five students in meters. Supposed
samples of size 2 are taken from this population of five students, complete
the given table and answer the following tasks. Construct the desired
tables needed for your solutions and answers.
Student
Height (X)
X2
Hazel Kim
1.47
2.16
Mee Ann Mae
1.58
2.50
Grace Ann
1.67
2.79
Jethro
69
1.51
2.86
Chelsea Mae
2.28
TOTAL
7.92
12.59
1. Solve for the mean of the population u.
2. Solve for the mean of the sampling distribution of the sample means µs.
3. Compare µ and ug.
4. Solve for the variance (o2) and the standard deviation (o) of the population.
5. Solve the variance (o²) and the standard deviation (a) of the sampling
distribution of the sample means lg.
6. Compare o and og.
108
![2/2322
b. Construct the sampling distribution table for the sample mear
and multiply the sample means to their probabilities.
Sample Mean
Frequency
Probability
X• P (X)
X
14
(x) d
1/15
14/15
1.
15
1/15
15/15
1.
2/15
32/15
17
2/15
34/15
18
3/15
54/15
2/15
2/15
38/15
40/15
21
1/15
21/15
1.
22
1/15
22/15
Total
15
15/15 or 1
270/15% 18
%3D
c. Solve for the mean of the sampling distribution of the sample
means by using the following formula u, = E[X• P(X)].
%3D
270
[(x)d • x]3 = *H
=18
15
Therefore, the mean of the sampling distribution of the
sample means is 18.
3. The population meanu is 18 and the mean of the sample means g
18. Therefore, u = g.
%3D
4. To solve for the variance (o?) and the standard deviation (o) of the
population, the given table below will be utilized.
8.
12
64
144
256
20
24
576
28
784
108
2 224](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F124d49b4-5fe1-47d0-96f9-476b688c779c%2Fa5c01de1-e882-43ad-82d4-94d85f3f73b7%2Fo00tcx9.jpeg&w=3840&q=75)
Transcribed Image Text:2/2322
b. Construct the sampling distribution table for the sample mear
and multiply the sample means to their probabilities.
Sample Mean
Frequency
Probability
X• P (X)
X
14
(x) d
1/15
14/15
1.
15
1/15
15/15
1.
2/15
32/15
17
2/15
34/15
18
3/15
54/15
2/15
2/15
38/15
40/15
21
1/15
21/15
1.
22
1/15
22/15
Total
15
15/15 or 1
270/15% 18
%3D
c. Solve for the mean of the sampling distribution of the sample
means by using the following formula u, = E[X• P(X)].
%3D
270
[(x)d • x]3 = *H
=18
15
Therefore, the mean of the sampling distribution of the
sample means is 18.
3. The population meanu is 18 and the mean of the sample means g
18. Therefore, u = g.
%3D
4. To solve for the variance (o?) and the standard deviation (o) of the
population, the given table below will be utilized.
8.
12
64
144
256
20
24
576
28
784
108
2 224
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