hw_ch6 solution

# hw_ch6 solution - MATH 2300 026 Homework#6 Name Due on 3rd...

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MATH 2300 026 Homework #6 Name___________________________________ Due on 3 rd November MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1. When a coin tossed three times, eight equally likely outcomes are possible as shown below. Let X denote the total number of heads obtained in the three tosses. Find the probability distribution of the random variable X. Leave your probabilities in fraction form. A) x| P(X = x) 0| 1/16 1| 1/4 2| 3/8 3| 1/4 B) x| P(X = x) 1| 1/4 2| 7/16 3| 1/4 C) x| P(X = x) 0| 1/8 1| 3/8 2| 3/8 3| 1/8 D) x| P(X = x) 0| 1/16 1| 3/16 2| 3/16 3| 1/16 E) x| P(X = x) 0| 0 1| 1/4 2| 3/8 3| 1/4 2. Suppose that two balanced dice, a red die and a green die, are rolled. Let Y denote the value of where G represents the number on the green die and R represents the number on the red die. What are the possible values of the random variable Y? A. - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5 B. - 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6 C. 0, 1, 2, 3, 4, 5, 6 D. 0, 1, 2, 3, 4, 5 3. The random variable X is the number of siblings of a student selected at random from a particular secondary school. Its probability distribution is given in the table. Find the mean of the given probability distribution. mean = g G ± ² ± ³´ µ¶ · = G ± ¸ = ¹ 0 × 7 24 º + ¹ 1 × 13 48 º + ¹ 2 × 3 16 º + ¹ 3 × 7 48 º + ¹ 4 × 1 16 º + ¹ 5 × 1 24 º = 1 .542 A. 1.438 B. 1.833 C. 2.5 D. 1.542 4. The area that lies between - 1.10 and - 0.36 A. 0.4951 B. 0.2237 C. 0.2259 D. 0.2239 E. 0.7763 5. Find the z - score for which the area under the standard normal curve to its left is 0.96 A. - 1.38 B. 1.75 C. 1.82 D. 1.03 E. - 1.75 Use the empirical rule to solve the problem. 6. The lifetimes of light bulbs of a particular type are normally distributed with a mean of 360 hours and a standard deviation of 5 hours. What percentage of the bulbs has lifetimes that lie within 1 standard deviation of the mean?

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hw_ch6 solution - MATH 2300 026 Homework#6 Name Due on 3rd...

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