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DIRECTION: Find the mean, variance, and standard deviation of the discrete random variable X with the following probability distribution.(5 points each)
1.
X P(X)
0 0.2
1 0.3
2 0.2
3 0.2
4 0.1
2.
X P(X)
0 0.004
1 0.435
2 0.355
3 0.206
3.
X P(X)
1 0.1
2 0.1
3 0.6
8 0.13
19 0.07
4.
X P(X)
6 0.1
8 0.11
9 0.61
10 0.09
11 0.09
Let the mean concentration of particulate matter collected on filter paper is
45.6 ppm, with the standard deviation is 4.4 ppm. Find the probability that the
mean concentration of particulate matter in a sample of 87 filter papers will be
within 47 ppm of the guideline level.
Rainfall data were collected for 12 months at Location A in mm, Jan 209, Feb
174, Mac 268, Apr 300, May 246, Jun 174, Jul 183, Aug 219, Sep 243, Oct 308,
Nov 373, Dec 284. According to the Department of Irrigation and Drainage
report, the average rainfall for the year of 2019 was 300mm. Find the T-score of
this sample.
Body temperature is known to have normal distribution among healthy adults.
A researcher collected data from a random sample of 20 healthy adults. It was
found that the sample temperatures have a mean of 88.4oF and a sample
standard deviation of 0.3oF.
identify the degrees of freedom (DF) for this study.
An analysis of the monthly allowances received by a sample of five engineers from a telco company has been conducted recently. The mean and median of the allowances is RM7000. A unimodal among the observations is RM12,000. Find the standard deviation if the allowances paid to each engineer were in full thousands.
a) Let the mean concentration of particulate matter collected on filter paper is 45.6 ppm, with the standard deviation is 4.4 ppm. Find the probability that the mean concentration of particulate matter in a sample of 87 filter papers will be within 47 ppm of the guideline level. (4 marks) b) Rainfall data were collected for 12 months at Location A in mm, Jan 209, Feb 174, Mac 268, Apr 300, May 246, Jun 174, Jul 183, Aug 219, Sep 243, Oct 308, Nov 373, Dec 284. According to the Department of Irrigation and Drainage report, the average rainfall for the year of 2019 was 300mm. Find the T-score of this sample. c) Body temperature is known to have normal distribution among healthy adults. A researcher collected data from a random sample of 20 healthy adults. It was found that the sample temperatures have a mean of 88.4oF and a sample standard deviation of 0.3oF. i.
A group of five boys and eight girls go to the fair. Admission cost nine dollars per person. Which expression does not show the total amount group will pay?
A construction crew is lengthening a road that originally measured 41
miles. The crew is adding one mile to the road each day.
Let
L
be the length (in miles) after D
days of construction. Write an equation relating
L
to D
.Then use this equation to find the length of the road after 37
days
The radius of a quarter circle is 7 meters. What is the quarter circle's perimeter?
Use 3.14 for 𝜋.
John deposits $450 at the end of every 3 months in a savings account. The account has a 5% interest compounded quarterly. How much will he have in his account at the end of 7 years and 3 months?
An analysis of the monthly allowances received by a sample of five engineers
from a telco company has been conducted recently. The mean and median of
the allowances is RM7000. A unimodal among the observations is RM12,000.
Find the standard deviation if the allowances paid to each engineer were in full
thousands
After several months of planting roses, Siti measures the height in centimeters
each of the plant. The height of the plants is given as below:
38, 14, 22, 36, 35, 29,19, 24, 32, 35, 41, 47
a) Construct a stem-and-leaf diagram for Siti’s data.
b) Calculate the mean, median, mode and range for Siti’s data
