MTH302 Long and Short Solved Questions

MTH302 Long Solved Questions

By

If you toss a die and observe the number of dots that appears on top face then write the events that the even number occurs.

Solution:

Number of Possible outcomes = 6 Number of Events = 3

P= Number of events/Number of all Possible outcomes. P= 3/6

Q43. Define Cumulative Poisson distribution. (2 marks)

Solution: A cumulative Poisson distribution is used to calculate the probability of getting atleast n successes in a Poisson experiment. Here, n is the Poisson random variable which refers to the number of success.

Formula:

P(x < n) = P(x = 0) + P(x = 1) + ... + P(x = n)

where, P(x = 0) and P(x = 1) is calculated using Poisson distribution formula.

Q44. Four friends take an IQ test. Their scores are 96, 100, 106, 114. Which of the following statements is true? Give reason. (3 marks)

I. The mean is 103. II. The mean is 104. III. The median is 100. IV. The median is 106.

(A) I only (B) II only (C) III only (D) IV only (E) None is true Solution: The correct answer is (B). The mean score is computed from the equation: Mean score = Σx / n = (96 + 100 + 106 + 114) / 4 = 104 Since there are an even number of scores (4 scores), the median is the average of the two middle scores. Thus, the median is (100 + 106) / 2 = 103

Q45. What is the probability that a bag filled by the machine weighs less than 515 g? z = (515 - 510)/2.5 = 2.0 (3 marks)

( Use the table given below )

Solution: Method is available in Lecture 40…..

=0.5+0.4772 = 0.9772

Q46. State three important properties of regression line (3 marks)

Solution: There are three important properties of regression line are as follows.\ Slope Intercept Straight Line Slope: The slope is the vertical distance divided by the horizontal distance between any two points on the line, which is the rate of change along the regression line.

n · xy · x · y · b · n · x · x

Intercept: Use the INTERCEPT function when you want to determine the value of the dependent variable when the independent variable is 0 (zero).

Straight Line: The simplest is the Simple Linear. Regression Model or a relationship between variables that can be represented by a straight line equation. Y=a+bX

Q47. Calculate the mean, median and mode for the following set of data 5, 6, -5, 8, 19, 2, 1, 6, 25 (5 marks)

Solution: X

-5

Q21. Define the Null Hypothesis. (2 marks)

Answer: Null hypothesis is a scenario which explain a given set of data. It is tested to determine whether data provides sufficient reasons to pursue some alternative hypothesis.