Course: Introduction to Statistics (BUS 172) Answer all the questions. [When using a formula, you must show the expression with the values plugged in the formula before providing the final answer] Question 1: [you must show the probability as fractions, e.g., 45/120] The following table shows the distribution of 122 companies by type and size. Type Size Smal Large Domestic 54 29 Foreign 8 31 (a) Suppose a company is selected at random. Then compute the probability that L. The company is domestic or it is large. II. The company is small and foreign. b) Are being domestic and being a small company independent events? (c) What is the value of P(domestic and foreign)? Justify your answer. (d) if two foreign firms are selected at random what is the probability that both are large? Question 2: According to the finding of a recent survey 74% of the university students in Bangladesh do not know how to swim. Suppose this result holds true for the current population of all Bangladeshi university students. Suppose a sample of 6 students is randomly selected. i. Which discrete probability distribution can be used in this situation and under which conditions ii. Find the probability that exactly 2 students in the sample do not know how to swim. iii. Find the probability that exactly 1 of the students in the sample knows how to swim. iv. Find the probability that at least 4 of the students in the sample do not know how to swim. Find the mean and standard deviation of X, where X is the number of students in the sample who do not know how to swim. Formula 1. u = Z x P(x) 6. P(A and B) = P(A) P(B/A) 2. 0= V E x2 P(x) - HZ 7. P(A or B) = P(A)+ P(B) - P(A and B) 3. P(x ) = n C xP* q n-x 4. u= nP and o = Vnp