The data set "stat 250 final exam scores" contains a random sample of 269 stat 250 students’ final exam scores (maximum of 80) collected over the past two years. answer the following questions using this data set.

a) what proportion of students in our sample earned b’s on the final exam? a letter grade of b is obtained with a score of between 64 and 71 inclusive. hint: you can do this many ways, but in statcrunch, go to data à row selection à interactive tools. in the slider selectors box, click the variable "scores" into the variable box. then click compute. use the slider to obtain the count by looking at the "# rows selected" presented in the first line of the box. show your work (i. e. describe the method you used to obtain the number of b’s) and express this value as a proportion rounded to four decimal places.

b) using the sample proportion obtained in (a), construct a 90% confidence interval to estimate the population proportion of students who earned a b on the final exam. do this "by hand" using the formula and showing your work ( type your work, no images accepted here). assume all central limit theorem conditions hold. round your confidence limits to four decimal places.

c) verify your result from part (b) using stat à proportions stats à one sample à with summary. inside the box, select confidence interval and click compute! copy and paste your statcrunch result in your document.