Finite Mathematics 1. A fair die is rolled three times. What is the probability of obtaining a 4,3, and 4, in that order? 2. A fair die is rolled four times. What is the probability of obtaining at least three 6's? 3. If a baseball player has a batting average of 0.355, what is the probability that the player will get the following number of hits in the next four times at bat? (A) Exactly 2 hits (Round to the three decimal places as needed. (B) At least 2 hits (Round to the three decimal places as needed) 4. A random variable represents the number of successes in 20 Bernoulli trials, each with probability of success p = 0.55. (A). Find the mean and standard deviation of the random variable. (B). Find the probability that the number of successes lies with 1 standard deviation of the mean. 5. Discuss the validity of the following statement. If the statement is always true, explain why. If not, give a counterexample. The mean of a normal distribution is a positive real number. Choose the correct answer below. A. The statement is false because the function f left parenthesis x right parenthesis equals StartFraction 1 Over 2 StartRoot 2 pi EndRoot EndFraction e Superscript StartFraction negative left parenthesis x plus 1 right parenthesis squared Over 8 End Fractionf(x)=122e(x+1)28 represents a normal curve and the mean is a negative number. A. The statement is false because the function f left parenthesis x right parenthesis equals StartFraction 1 Over negative 2 StartRoot 2 pi EndRoot EndFraction e Superscript StartFraction negative left parenthesis x plus 1 right parenthesis squared Over negative 8 EndFractionf(x)=122e(x+1)28 represents a normal curve and the mean is a negative number. B. The statement is true because all probabilities must be positive. C. The statement is true because the mean is found by using the square root, which always results in a positive number. 6. Discuss the validity of the following statement. If the statement is always true, explain why. If not, give a counterexample. The area under a normal distribution and above the horizontal axis is equal to 1. Choose the correct answer below. A. The statement is true because all normal distributions have the same shape. B. The statement is false because the area under the normal curve with a mean equal to 1 and a standard deviation equal to 2 does not equal 1. C. The statement is true because the graph of a normal distribution is a normal curve, and irrespective of theshape, the area between the normal curve and the x-axis is always 1. D. The statement is false because the area under the normal curve with a mean equal to minus1 and a standard deviation equal to 2 does not equal 1. 7. Salespeople for a solar technology company have average annual sales of $ 300,000, with a standard deviation of $20,000. What percentage of the salespeople would be expected to make annual sales of $350,000 or more? Assume a normal distribution. 8. In a certain college, 33% of the math majors belong to foreign student. If 10 students are selected at random from the math majors, that is the probability that no more than 6 are foreign? Round answer to four decimal places. A. 0.9846 B. 0.9130 C. 0.9815 D. 0.0547