BIT Basic Statistics

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?

A data analytics company is analyzing the server latency times (in milliseconds) from a cloud-based application. They collect the following latency times in milliseconds from 10 requests during peak usage hours: 120, 135, 150, 125, 140, 160, 170, 155, 165, and 150. 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.

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). The data collected over 10 projects is as follows:

(a) Calculate the Pearson correlation coefficient to determine the strength and direction of the linear relationship between the number of hours spent on coding and the number of bugs encountered.

(b) Find the regression equation of bugs encountered on hours spent on coding.

(c) Predict the number of bugs encountered if an employee spends 48 hours coding based on the regression equation.

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.

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?

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.

A database server has a 95% reliability rate, meaning it functions without failure 95% of the time. However, even if the server does not fail (works properly), there is a 5% chance that it will still report an error (false positive). If the server reports an error, what is the probability that the server has actually failed?

The resolution time for customer support queries follows a normal distribution with a mean of 30 minutes and a standard deviation of 5 minutes.

(a) What percentage of queries are resolved in less than 25 minutes?

(b) What percentage of queries are resolved between 25 and 35 minutes?

The time taken (in seconds) to complete a file transfer operation is recorded for 11 sessions: 100, 120, 110, 115, 130, 105, 125, 122, 112, 108 and 135. Calculate the five-number summary for this data and construct a box plot.

A tech support team handles the following number of customer queries (X) per hour, along with their associated probabilities:

Find the expected number and variance of queries handled by the team in an hour.

Discuss the importance of statistics in the field of information technology.

Write a short note on the following:

(a) Sampling Error

(b) Stratified sampling