I guess I was hoping if anybody could check my work? This is a 4 part question, I hope I am not breaking rules by posting so much?? I took most of them as far as I could, a couple I am completely clueless on....!
Suppose that for a school, distances between students' homes and school observe a normal distribution, with mean 4.76 miles and standard deviation being 1.76 miles.
a) What percentage of students live farther than 6.78 miles from the school?
Z=X-mean/std --> 6.78-4.76/1.74= 1.16
0.5- 0.3770= 0.123
Thus, 12.3% of students live farther than 6.78 miles from the school.
(yes? no? i think i may have got the right answer for that one)
b) A survey shows that 8% of students who live closest to the school chose to walk to the school. What is the maximum walking distance of these 8% of students? In other words, what is the distance below which these 8% of students walk to school?
(I really don't know how to start on this one, could anybody set me in the right direction?)
c) Suppose there is a new policy that allows students living beyond 4.50 miles to take a bus to school. There are 3,567 students enrolled. How many students are not eligible to take school buses?
Z=4.5-4.76/ 1.74= -0.15
0.50 + 0.0596 = 0.5596 or 55.96%
0.4404 * 3567= 1570.91 = 1571
Thus, approximately 1,571 students are not eligible to take school buses.
d) Suppose all samples of size 12 are taken. What percentage of sample means has a value larger than 6.78 miles?
*Since this one is talking about sample means, to find the z-score is:
Z=Mean-Mean of sample means/ std of sample means, so
Z=6.78-4.76/ (1.74/[sqrt]12)= 4.02
I get lost here, because how am I supposed to find a z-score of 4.02 in my table? *bangs head* Anybody?