سوال 2۔ میر کے سوانحی حالات و کوائف قلم بند کیجیے
See Answer →سوال 1۔ غالب کی غزل گوئی سے بحث کیجیے
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Explain the purpose of control charts in Statistical Quality Control (SQC). Differentiate between a pchart and a c-chart with respect to the type of data they monitor.
See Answer →Explain the purpose of control charts in Statistical Quality Control (SQC). Differentiate between a pchart and a c-chart with respect to the type of data they monitor.
| Year | Q1 | Q2 | Q3 | Q4 |
|---|---|---|---|---|
| 2022 | 30 | 40 | 36 | 44 |
| 2023 | 34 | 46 | 40 | 50 |
| 2024 | 38 | 52 | 46 | 56 |
The quarterly sales (in thousands of units) of a company from 2022 to 2024 are given below. Calculate the 4-quarterly moving averages to determine the trend.
| Year | Q1 | Q2 | Q3 | Q4 |
|---|---|---|---|---|
| 2022 | 30 | 40 | 36 | 44 |
| 2023 | 34 | 46 | 40 | 50 |
| 2024 | 38 | 52 | 46 | 56 |
An e-commerce company wants to test three different website layouts (Layout A, Layout B, Layout C) to see if they have a significant effect on the average time (in minutes) a user spends on the site. The following data was collected from different user groups:
| Layout A | Layout B | Layout C |
|---|---|---|
| 8 | 12 | 13 |
| 10 | 11 | 15 |
| 9 | 10 | 14 |
| 11 | 13 | 16 |
| 7 | 9 | 12 |
Perform a one-way ANOVA to test the hypothesis that there is no significant difference between the mean user session times for the three layouts at a 5% level of significance.
(Given F-critical value F(2, 12) at α=0.05 is 3.89).
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A random sample of size 100 is taken from a large population. The sample mean is found to be 150 and the population standard deviation is known to be 20. Construct a 95% confidence interval for the population mean. (Given Z₀.₀₂₅ = 1.96).
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Explain the key differences between Simple Random Sampling, Stratified Sampling, and Cluster Sampling. Provide a suitable example for each to illustrate its application.
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A survey was conducted to determine if there is a relationship between a person's age group and their preferred mode of online payment. The results are tabulated below:
| Age Group | UPI | Credit/Debit Card | Net Banking | Total |
|---|---|---|---|---|
| 18–30 | 150 | 60 | 40 | 250 |
| 31–45 | 80 | 70 | 50 | 200 |
| 46–60 | 40 | 50 | 60 | 150 |
| Total | 270 | 180 | 150 | 600 |
Using the Chi-Square (χ²) test, determine whether the preferred mode of payment is independent of the age groupat a 5% level of significance.
(Given χ² critical value for 4 degrees of freedom at α=0.05 is 9.488).
See Answer →A manufacturer of LED bulbs claims that the average lifespan of their bulbs is 8000 hours. A random sample of 50 bulbs is tested, and it is found that their average lifespan is 7950 hours with a standard deviation of 120 hours.
Test the manufacturer's claim at a 5% level of significance. State your null and alternative hypotheses clearly. (Given Z₀.₀₂₅ = 1.96 for a two-tailed test).
See Answer →A call center receives an average of 4 calls per minute. Assuming a Poisson distribution, find the probability that in a given minute, the call center receives:
(i) Exactly 2 calls.
(ii) At most 1 call.
(Given e⁻⁴ ≈ 0.0183)
See Answer →A software company has two divisions, A and B, developing mobile apps. Division A develops 60% of the apps, and Division B develops 40%. It is known that 5% of apps from Division A have bugs, while 8% of apps from Division B have bugs. If an app selected at random is found to have a bug, what is the probability that it was developed by Division A?
See Answer →To study the relationship between the number of hours spent studying per week and the marks obtained in an examination, a sample of 10 students was taken. The data is as follows:
| Study Hours (X) | 5 | 8 | 10 | 12 | 15 | 4 | 7 | 9 | 11 | 14 |
|---|---|---|---|---|---|---|---|---|---|---|
| Marks (Y) | 55 | 70 | 75 | 80 | 90 | 50 | 65 | 72 | 78 | 85 |
(a) Calculate the Karl Pearson's coefficient of correlation between Study Hours and Marks.
(b) Determine the two regression equations (Y on X and X on Y).
(c) Predict the marks of a student who studies for 13 hours a week.
See Answer →The following table shows the distribution of response times (in milliseconds) for a web server over a period of 100 requests:
| Response Time (ms) | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 |
|---|---|---|---|---|---|---|
| Number of Requests | 8 | 15 | 25 | 30 | 12 | 10 |
(a) Calculate the Mean and Median response time.
(b) Calculate the Standard Deviation of the response times.
(c) Draw a Histogram for the given data.
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In A ‘Cup of Tea’ by Katherine Mansfield, the emphasis is on situations rather than thecharacter. Comment on the plot and style of the story.,
See Answer →Comment on: The ‘Yellow Wallpaper’ as a self-confessional, psychological thriller.
See Answer →What does the kitchen mean to different women and men? Comment on the symbolicimportance of the kitchen in ‘A Kitchen in the Corner of the House’, by C.S. Lakshmi.
See Answer →‘Sunlight on a Broken Column’ works through juxtapositions, parallels and polarities.Elaborate.
See Answer →Discuss the themes of Dickinson’s poems.
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