Question

can someome explain how to do the problem 1.106 and 1.108 please and thanks

7 re) > 1.77 (d)-2.25 - 1.77 1.106 ) Find the number such that the proportion of observations that are less than in a standard Normal distribution is 0.8. (b) Find the number z such that 35% of all observations from a standard Normal distribution are greater than z. 1.107 NCAA rules for athletes. The National Collegiate Athletic Association (NCAA) requires Division I athletes to score at least 820 on the combined Mathematics and Verbal parts of the SAT to compete in their first college year. (Higher scores are required for students with poor high school grades.) In 2000, the scores of the 1,260,000 students taking the SATS were approximately Normal with mean 1019 and standard deviation 209. What percent of all students had scores less than 820? 08 More NCAA rules. The NCAA considers a student a "partial qualifier" eligible to practice and receive an athletic scholarship, but not to compete, if the combined SAT score is at least 720. Use the information in the previous exercise to find the percent of all SAT scores that are less than 720.

Answer 1

Solution-1.106: Part-A: Value of z-score such that area under the normal curve to the left of it equal to 0.8, is given by: z = 0.842 Hence, the value of 'z', such that the proportion of observations that are less than 'z' in a standard normal distribution is 0.8, is given by = 0.842 Part-B: Value of z-score such that area under the normal curve to the right of it equal to 35%, is given by: z = 0.385 Hence, the value of 'z', such that 35% of all observations from a standard normal distribution are greater than 'z', is given by = 0.385 Solution-1.108: Mean = p = 1019 Standard deviation = 0 = 209 Percentage of SAT scores that are less than 720 = P(x < 720) Z-score for (x = 720): Z =- 220 – 1019 Z= 209 > z= -1.431 Hence, P(x < 720) = P(Z < -1.431) From normal distribution table; P(Z < -1.431) = 0.0763 Hence, percentage of all SAT scores that are less than 720 = 7.63%