Applications

ApplicationsExercises extracted from Mathematical Statistics 6th Ed.by John E. FreundsQuestion 1A random sample of size n=64 is taken from a normal population with a mean 51.4 and s.d. 6.8. What is the probability that the mean of the sample will (a) exceed 52.9;(b) fall between 50.5 and 52.3;(c) be less than 50.6? Question 2A random sample of size 100 is taken from a normal population with s.d. 25. What is the probability that the mean of the sample will differ from the mean of the population by 3 or more either way?Question 3A random sample of size n=200 is taken from a uniform population with a=24 and b=28. Based on the central limit theorem (CLT), what is the probability that the mean of the sample will be less than 35?

Question 4A random sample of size n=225 is taken from an exponential population with =4. Based on the central limit theorem (CLT), what is the probability that the mean of the sample will exceed 4.5?

Question 5Question 6Question 7Question 8Integrate the appropriate Chi-square density to find the probability that the variance of a random sample of size 5 from a normal population with population variance 25 will fall between 20 and 30.Question 9The claim that the variance of a normal population is 25 is to be rejected if the variance of a random sample of size 16 exceeds 54.668 or is less than 12.102.What is the probability that this claim will be rejected even though population variance is 25?Question 10A random sample of size n=25 from a normal population has the sample mean 47 and s.d. 7. Can we say that the given information supports the estimation that the mean of the population is 42?