3. In a survey of top executives, it was found that 46% had either traveled internationally on business or could fluently speak a foreign language. The probability that an executive who had not traveled internationally could speak a foreign language was 10%. It was found that only 4% of the executives had traveled internationally and could speak a foreign language. a) What is the probability that an executive who has traveled internationally speaks a foreign language fluently? b) What is the probability that an executive who speaks a foreign language fluently has traveled internationally? c) What is the probability that an executive has traveled internationally and could not speak a foreign language fluently? THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: 4. The probability that a person catches a cold during the cold and flu season is 0.4. Assume that 10 people are chosen at random. a) What is the probability that four or more of them will catch a cold? b) What is the standard deviation for the number of people catching a cold? THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: 5. The number of people arriving at a bicycle repair shop follows a Poisson distribution with an average of 5 arrivals per hour. Let X represent the number of people arriving per hour. a) What is the probability that at most seven people arrive at the bike repair shop in a one hour period of time? b) What is the probability that more than seven people arrive at the bike repair shop in a one hour period of time? THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: 6. Let the random variable X follow a normal distribution with mean = 48 and variance 2 = 60.84. a) Find the probability that X is greater than 58. b) Find the probability that X is greater than 36 and less than 60. c) Find the probability that X is less than 52. THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: 7. Let the random variable Z follow a standard normal distribution. a) What is P(Z > 0.29)? b) What is P(Z < 1.23)? c) What is P(Z > -0.52)? d) What is P(-0.44 < Z < 1.2)? 8. Three applicants are to apply for 3 houses independently. What is the probability that (a) All the 3 apply for the same house (b) They apply for different house 9. In a normal distribution 31% of the items are under 45 and 8% are over 64. Find the mean and standard deviation of the distribution? 10. Salesman is known to sell a product in 3 out of 5 attempts while another salesman in 2 out of 5 attempts. Find the probability that (a) No sale will be effected when both try to sell the product; (b) Either of them will succeed in selling the product