Question

Students at SHSU have an average GPA of 2.78 with a standard deviation of 0.65. You have been tasked by the university president to select a random sample of students, and to conduct in-depth interviews with them about how their academics were impacted by COVID-19. We would like the random students that you select to be representative of the entire student body, and therefore the GPA of your sample should be within 0.1 grade points of the population mean. How many students should you randomly select for interviews if you want to be 99% sure that the mean GPA of your interviewees is between 2.68 and 2.88?

Answer 1

& Solution - Let x Avg GPA of studest. We assume XN N(M=2.78, 82 = 0.652) we know that XSN (M, 82) Here XNM= 2.78, 22 0.65%) It is gives that pl 2-685X52.88) = a.gg P{2-68 - 1 X-M { 0-99 لک 2.88-07- - p[ 2-68 – 2-78 FZS 2.88 -2.78 ] = 0.99 0.65 W 0.6515 ) – 22 (22-88 – 2.78 7 ogg (due of symmetry 0.65155 of normal dista 1 - 2P (270.15385)=0-99 2PCZYo'ls38 5)=0.01 Plz> 0.15 3855)=0.005 O. 1538 5 = 2.58 (from ste nomal table) n = 16.775 in 281.4017 In 2811 28) studests should be randomly selected for internews.