StudyNp | BIT Second Semester – 2081 Question for Basic Statistics

Credit:

Eli Tamang

Tribhuwan University

Institute of Science and Technology

2081

Bachelor Level / First Year / Second Semester / Science

Bachelors in Information Technology (STA154)

(Basic Statistics)

Full Marks: 60

Pass Marks: 24

Time: 3 Hours

Candidates are required to give their answers in their own words as for as practicable.

The figures in the margin indicate full marks.

Section A

Long Answers Questions

Attempt any TWO questions.

[2*10=20]

A cloud service provider is evaluating the response times of two different server clusters over 10 requests. The company wants to compare the variability in response times between the two clusters. Here are the response times (in milliseconds) for the two clusters. Which cluster has more consistent response times?

\begin{array}{|c|cccccccccc|}\hline \text{Cluster A} & 88 & 92 & 94 & 85 & 90 & 95 & 89 & 87 & 91 & 86 \\ \hline \text{Cluster B} & 130 & 135 & 132 & 140 & 128 & 133 & 137 & 131 & 129 & 138 \\ \hline \end{array}

[10]

Compute four central moments and hence find the mean, standard deviation, the measure of skewness, and the measure of kurtosis from central moments. Also, comment on the nature of the data.

120, 135, 150, 125, 140, 160, 170, 155, 165, 150

[10]

A software company tracks the number of hours its employees spend on coding (X) and the corresponding number of bugs they encounter during testing (Y).

\begin{array}{|c|cccccccccc|}\hline \text{Hours (X)} & 20 & 25 & 30 & 35 & 40 & 45 & 50 & 55 & 60 & 65 \\ \hline \text{Bugs (Y)} & 5 & 7 & 8 & 12 & 15 & 13 & 17 & 18 & 20 & 25 \\ \hline \end{array}

(a) Calculate the Pearson correlation coefficient. (b) Find the regression equation of Y on X. (c) Predict the number of bugs encountered if an employee spends 48 hours coding. [10+0]

Section B

Short Answers Questions

Attempt any Eight questions.

[8*5=40]

In a survey of 50 IT students, the following programming languages were preferred: Python (20), Java (15), C++ (10), and JavaScript (5). Create a pie chart representing the preferences. [5]

A server records the number of requests per minute, which follows a Poisson distribution with a mean of 5 requests per minute. (a) What is the probability that exactly 3 requests occur in a given minute? (b) What is the probability that more than 2 requests will occur?

\lambda = 5

[5]

A sample survey of 80 customers shows that 56 are satisfied with an IT service. Estimate the proportion of satisfied customers in the population with a 95% confidence interval.

n = 80, \quad x = 56

[5]

A database server has a 95% reliability rate. Even if the server does not fail, there is a 5% chance that it will still report an error. If the server reports an error, what is the probability that the server has actually failed?

P(\text{Failure}) = 0.05, \quad P(\text{False positive}) = 0.05

[5]

The resolution time for customer support queries follows a normal distribution with mean 30 minutes and standard deviation 5 minutes. (a) What percentage of queries are resolved in less than 25 minutes? (b) What percentage are resolved between 25 and 35 minutes?

\mu = 30, \quad \sigma = 5

[5]

The time taken (in seconds) to complete a file transfer operation is recorded for 11 sessions. Calculate the five-number summary and construct a box plot.

100, 120, 110, 115, 130, 105, 125, 122, 112, 108, 135

[5]

10.

A tech support team handles the following number of customer queries (X) per hour along with their probabilities. Find the expected number and variance of queries handled per hour.

\begin{array}{|c|ccccc|}\hline X & 0 & 1 & 2 & 3 & 4 \\ \hline P(X) & 0.10 & 0.20 & 0.30 & 0.25 & 0.15 \\ \hline \end{array}

[5]

11.

Discuss the importance of statistics in the field of information technology. [5]

12.

Write a short note on: (a) Sampling Error (b) Stratified sampling. [5]