PLEASE ANSWER ALL THE PROBLEMS CORRECTLY. SHOW COMPLETE SOLUTIONS. THANKS

Problem solving. (Show your complete solution) 1. Forty students have been given the following grades in a Field study. Assume that they come from a population that has the shape of a normal distribution and standard deviation is 6. Estimate their true grades, using 99% confidence. Find the point estimate, standard error, lower and upper interval estimates. 92 84 93 90 92 93 94 90 90 94 87 83 95 85 87 85 95 84 89 16 89 93 87 83 87 80 90 84 83 82 80 90 83 80 89 88 81 81 93 90 2. Anna wants to know the mean of all entering trainees in a boot camp. The mean age of a random sample of 25 trainees is 18 years and the standard deviation is 1.3 years. The sample comes from a normally distributed population. Use a = 0.1 to find the following: a. Point estimate b. Standard Error c. Interval estimate 3. In a survey of 500 random families in a particular subdivision, mothers are asked if they use cell phones to communicate. There are 426 who have said YES. Use a 95% confidence to estimate the proportion of all mothers who use the cell phone to communicate. Compute the point estimate, error and interval estimate