IGNOU BCS 40 SOLVED ASSIGNMENT

Ques 1.

The following table shows the distribution of response times (in milliseconds) for a web server over a period of 100 requests:

(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.

Ques 2.

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:

(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.

Ques 3.

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?

Ques 4.

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)

Ques 5.

 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).

Ques 6.

 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:

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).

Ques 7.

 Explain the key differences between Simple Random Sampling, Stratified Sampling, and Cluster Sampling. Provide a suitable example for each to illustrate its application.

Ques 8.

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).

Ques 9.

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:

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).

Ques 10.

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.

Ques 11.

 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.

Ques 12.

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.

Ques 13.

The following table shows the distribution of response times (in milliseconds) for a web server over a period of 100 requests:

(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.

Ques 14.

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:

(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.

Ques 15.

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?

Ques 16.

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)

Ques 17.

 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).

Ques 18.

 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:

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).

Ques 19.

 Explain the key differences between Simple Random Sampling, Stratified Sampling, and Cluster Sampling. Provide a suitable example for each to illustrate its application.

Ques 20.

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).

Ques 21.

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:

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).

Ques 22.

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.

Ques 23.

 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.

Ques 24.

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.

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