Question 698347
For each section, you'll need to find a z-value or set of z-values, and use a table to find the appropriate probabilities.<br>

{{{Z = (X - mu)/sigma}}}, where X is the value, mu; is the mean, and sigma is the standard deviation.<br>

1) {{{Z = (90 - 75)/8 = 1.875}}}. If you look up Z = 1.88 (most Z-tables round to the nearest hundreth) on a Z-table such as http://lilt.ilstu.edu/dasacke/eco148/ztable.htm, you will get the value .9699. The value on the Z-table given is the probability that a random Z-value is less than the Z-value on the table. Thus, the probability the student scores less than 90 is .9699, and the probability he scores above 90 is 1 - .9699 = .0301.
2) {{{Z = (80 - 75)/8 = .625}}}. The probability on the Z-table corresponding to Z = .63 is .7357. Again, since this is the probability that the value has a lower Z-score than .63, the probability the student scores above an 80 is 1 - .7357 = .2643. In order to find the probability of scoring between 80-90, you will need to subtract the probability the student scores above a 90 from the probability the student scores above an 80. This value is .2643 - .0301 = .2342.
30 {{{Z = (60 - 75)/8 = -1.875}}}. Reading the value of Z = -1.88 from the table gives the value .0301. Since the table gives the probability of a score lower than the Z-value, and this is the value you are looking for in this case, the probability of scoring less than 60 is read directly from the table and is equal to .0301.