Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of 550 and a standard deviation of 100. Find the probability that a student will score:
(a) Over 660.0.
(b) Less than 360.
(c) Between 400 and 700.0.
Correct answer receives best answer, please do your best to show your work so I can understand.
Thanks.
(a) Over 660.0.
(b) Less than 360.
(c) Between 400 and 700.0.
Correct answer receives best answer, please do your best to show your work so I can understand.
Thanks.
-
what i think you can do is find the z-score.
you have the population mean u = 550 and the population SD = 100
z-score = (X - u)/SD <<<<< (score - population mean)/population SD
you will have to look at a z-table to find the z-score and find the % under the curve...remember that the z-score calculates percentages from the mean to the z-score. some of these you will have to subtract to find the percent area under the tail
a) (660-550)/100 = 1.1 = z-score
looking at a table of z-scores...you find that the % associated with it is 36.43%, however, the question asks for score over 660..so you don't want the % below it (which would be 50 + 36.43) instead do subtraction 50% - 36.43% = 13.57% or 0.1357 probability of getting a score over 660 (i.e. the area under the right tail)
the rest are pretty much doing the same....finding the z-score and then determining which shaded area you want. In other words, for less than 360, you want the negative tail. For btw 400 and 700, you can calculate the z-score separately for 400 and 700, find the separate %s and then combine/add them.
hope this is helpful.
.
you have the population mean u = 550 and the population SD = 100
z-score = (X - u)/SD <<<<< (score - population mean)/population SD
you will have to look at a z-table to find the z-score and find the % under the curve...remember that the z-score calculates percentages from the mean to the z-score. some of these you will have to subtract to find the percent area under the tail
a) (660-550)/100 = 1.1 = z-score
looking at a table of z-scores...you find that the % associated with it is 36.43%, however, the question asks for score over 660..so you don't want the % below it (which would be 50 + 36.43) instead do subtraction 50% - 36.43% = 13.57% or 0.1357 probability of getting a score over 660 (i.e. the area under the right tail)
the rest are pretty much doing the same....finding the z-score and then determining which shaded area you want. In other words, for less than 360, you want the negative tail. For btw 400 and 700, you can calculate the z-score separately for 400 and 700, find the separate %s and then combine/add them.
hope this is helpful.
.