Solve the following problems. Compute for the mean and standard deviation of the distribution and construct the corresponding normal curve. Note SHOW solution: 1. Compute the mean and standard deviation of the normal distribution where 68.3% of the values fall between 2.8 and 4.0. Construct the normal curve of the normal distribution. 2. Assume that 95.5% of students have a grade in Statistics and Probability subject between 85 and 93 and the data are normally distributed. (a.) Compute the mean and standard deviation of the distribution. (b.) Construct the normal curve of the normal distribution Directions: Find the indicated area under the normal curve, then convert it to percentage. Show solution 1. What percent of the area under the normal curve is between z = 0.58 and z = 2.8? 2. What percent of the area under the normal curve is between z = -2.00 and z = 2.00? 3. What percent of the area under the normal curve is between z = -1.15 and z = 1.15? 4. What percent of the area under the normal curve is between z = -1.34 and z = - 2.13? 5. What percent of the area under the normal curve is between z = 2.38 and z = -1.32? Direction: Solve the following problems: Show solution; 1. On a final examination in Statistics, the mean was 86 and the standard deviation is 4. Determine the standard score of the student who received a score of 92 assuming the scores are normally distributed. 2. Ben gets a score of 75 in a Chemistry test and 70 in a Physics test. Scores in a Chemistry test have a mean of 65 and a standard deviation of 6. Scores in the Physics test have a mean of 66 and a standard deviation of 2. In which subject is her standing better assuming that the scores in the two subjects are normally distributed? 3. In a Mathematics test, the mean is 50 and the standard deviation is 5. Assuming the scores are normally distributed, what percent of the scores is: a. greater than 55? b. less than 60? c. between 40 and 55