The variance of the SAT scores for all students who took that test this year is 5000. The varianceoftheSATscoresfor arandomsampleof20 studentsfromoneschool isequal to 3175.

1. Test at the 5% significance level whether the variance of the SAT scores for students from thisschool is lower than 5000. Assume that the SAT scores for all students at this school are(approximately)normally distributed.
2. Construct the 99% confidence intervals for the variance and the standard deviation of SATscoresfor allstudents at this school.

Draw picture if necessary. I will mark you as best and helpful. Please solve the math correctly as soon as possible.