Statistics and Probability Questions 2022

Running head: Statistics and probability 1
Statistics and Probability
Course code
Student name
Tutor

Statistics and Probability 2
QUESTION 1
1. Sample frequency mean and standard deviation
Mean 323.33
Std deviation 14.696
Table 1
2. Median, first and third quartile
Median 324
1st
Quartile 313.5
3rd
Quartile 334.5
Table 2
3. Since the mean and the median are almost equal, it can be concluded that the data is
approximately normally distributed.
4. Frequency polygon, histogram and cumulative frequency polygon
Frequency polygon
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0
10
20
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70
80
90
Frequency polygon
Lifetime in seconds
Frequency
Figure 1

Statistics and Probability 3
Histogram
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0
10
20
30
40
50
60
70
80
90
Histogram
Lifetime in seconds
Frequency
Figure 2
Cumulative frequency polygon
303 309 315 321 327 333 339 345
0
50
100
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200
250
300
cumulative frequency polygon
Figure 3
QUESTION 2
1.

Statistics and Probability 4
Mean = 200.24
Standard deviation = 3.75
X = 200
Z= x −μ
σ
Z=200.24−200
3.75 =0.064
P value corresponding to a Z-value of 0.064 for a two-tailed test at 0.05 level of significance is
0.94897
2. Hypothesis
H0: μ = 200
H1: μ ≠ 200
Alpha = 0.05
3. The structure of the test becomes a two-tailed test since the mean can either be greater or less
than 200 grams.
4. Since the p-value (0.95) is greater than the level of significance, the null hypothesis is not
rejected. It is concluded that the mean weight of the packets is 200 grams.
5.
Mean = 199.16
Standard deviation = 2.76
X = 200
Z= x −μ
σ
Z=5−2.76
3.75 =0.597
P value corresponding to a Z-value of 0.597 for a two-tailed test at 0.05 level of significance is
0.5505