BCA Probability & Statistics

What do you understand by data? Distinguish between primary and secondary data.

The following table represents the marks of 100 students

If the mean is 48, find the missing frequencies.

Define correlation. In order to find the correlation coefficient between two variable X and Y from 13 pairs of observations, following calculation are made:

\(\sum X = 30\), \(\sum Y = 5\), \(\sum X^2 = 670\), \(\sum Y^2 = 285\), \(\sum XY = 334\)

On subsequent verification, it was found that the pair (11, 4) was copied wrongly. The correct being (10,14), find the correct value of correlation coefficient.

Define regression. Estimate the blood pressure using the given data when age is 65.

Define Poisson distribution and state the conditions under which it is applicable. A telephone switch board of a company receives an average of 4 phone calls in 10 minutes interval. What is the probability of receiving

(i) exactly 3 calls in a 10 minutes interval

(ii) at most 2 calls in half an hour interval.

Suppose the sample standard deviation of response times (in milliseconds) for a web server is 12 ms. If we want to estimate the average response time with 99% confidence and margin of error of 3 ms, how many observations should be included in the sample?

Define sampling. Distinguish between census survey and sample survey.

What are the various methods of measuring dispersion in Statistics? In two factories A and B engaged in similar type of industry, the average weekly wages and variance are given below:

i. Which factory pays larger amount as weekly wages?

ii. Which factory shows greater variability in the distribution of weekly wages?

iii. What is the mean, standard deviation and variance of all the workers' wages in two factories taken together?

The number of emails sent per week by employees of a software company follows a normal distribution with mean 80 and standard deviation 16. Find:

(i) the probability that an employee sends at least 100 emails in a week

(ii) the probability that an employee sends at most 120 emails in a week.

(iii) the probability that an employee sends between 85 and 95 emails in a week.

The following table gives the data on the performance of three different detergents at three different water temperatures. The performance was obtained on the ‘whiteness’ reading based on specially designed equipment for nine loads of washing:

Perform a two-way analysis of variance, using the level of significance 0.05.