pls answer

Construct the probability distribution for the random variable described. (5 Points) Direction: Sketch and identify the areas of the regions under the normal Three coins are tossed. Let X be the random variable that represents the number of tails that will occur. curve corresponding to the following standard normal values or z - values: Find the values of random variable X and Construct the probabilty distribution. 1. to the left of z = 0 2. to the left of z = -1.14 Refer to the problem above. Choose the letter of the correct answer. 3. to the left of z = 2.3 6. What is the probability that there will be three heads? 4. between z = -1 and z = 3 a. k b. 2/3 C. 4/8 d. 1/8 5. between z = -3 and z = 3 7. What is the probability that there will be at least 1 head? a. 2/8 b. % c. 1/2 d. 7/8 8. What is the probability that there will be no head? Part II Multiple Choice a. 1/8 b. 5/6 d. 6/8 1. About how many percent of the area under the standard normal curve falls within 1 standard 9. What is the probability that there will be at most 2 head? deviation from the mean? a. 3/8 b. 5/6 c. 1/3 d. 7/8 a. 68.26% b. 95.44% c. 99.74% d. 53.5% 10. What is the probability that there will be at most three head? a. 1/8 b. 3/8 2. About how many percent of the area under the standard normal curve falls within 2 standard C. 1 d. 0 deviations from the mean. a. 68.26% b. 95.44% c. 99.74% d. 53.5% Part II 15 points 3. About how many percent of the area under the standard normal curve falls within 3 standard deviations from the mean. Compute for the Mean, Variance and Standard Deviation of the following probability distribution. Show a. 95.44% b. 53.5% C. 81.43% d. 99.74% your solution. Use decimal up to 6 digits. m N 4. Which of the following situations satisfies the condition of a normal curve. 0.10 0.20 0.45 0.25 a. mean and mode are equal, and median is greater than the two b. mean and median are equal, and mode is greater than the two X P(x) X . P(x) X - H (x - 1)2 c. median and mode are equal, and mean is less than the two (x - 1)2 . P(x) d. mean, median and mode are all equal. 5. What is the area under the normal curve which corresponds to the z-value of 2.54? a. 0.9938 b. 0.9945 c. 0.8375 d. 0.9905 Ex. P(x)] E[(x - H)?. P(X)] =