Solve the following word problems involving normal distribut

Solve the following word problems involving normal distribution. 1. A class of 50 students has mean score in the recent quiz of 72 with a standard deviation of 6. a. What would be the proportion of students who obtained scores between 60 and 75? b. How many percent is less than 70? How many students? c. How many percent is higher than 80? How many students? d. If a score is equivalent to z=-1.25, what is the raw score? 2. The weights of 80 female’s students aged 15 to 20 have a mean of 120 pounds, and a standard deviation of 6 pounds. a. What percent of the students have weights below 110 pounds? b. How many students have weights above 130 lbs.? c. How many students’ weights between 100 and 123 pounds? Solve the following word problems involving sampling distribution. 3. A random sample of size 625 was selected from a large population with a population mean of 15 and variance of 20.25. Compute the standard error and mean of the statistics. 4. Consider a sample size of 5 from this population: 5 6 8 10 12 13 a. How many samples can be formed from the N? b. Solve for the population variance. c. Compute for the statistics mean, and variance. 5. An electrical company claims that the average life of the bulbs it manufactures is 1,200 hours with a standard deviation of 250 hours. If a random sample of 100 bulbs is chosen, what is the probability that the sample mean will be: a. Greater than 1,150 hours? b. Less than 1,250 hours? c. Between 1,150 and 1,250 hours?