The class average on a math test was 82 with a standard deviation of 5. If the data is normally distributed, select all the true statements

Question

1. A z-score of 2.6 would be a test score of 95
2. About 68% of the students scored below a 87
3. A student scoring 74 would have a z-score of -1.6
4. About 25% of the class scored above 92
5. About 16% of the class scored 77 or below

Answer 1

1. a z-score of 2.6, would be 2.6 standard deviations above the mean or 82 + 2.6 * 5 = 95, true
2. using standardized z score: z = (x - mean)/SD and standard normal probability table

z = (87 - 82/5) = 1. corresponds to 0.8413, so 84% score below 87, false

3 z = (74 - 82)/5 = -1.6, true

4 z = (92 - 82)/5 = 2, corresponds to probability of 0.9772. So 97.72% scored below and 2.28% scored above, false

1. z = (77- 82)/5 = -1, corresponds to 0.1587 probability, so about 16% scored below 77, true