Final answer:
a. False. In a normal distribution, the percentage of scores greater than a specific z-score can be found using a standard normal distribution table. b. True. The percentile rank for the mean in any normal distribution is always 50%. c. True. A z-score represents the number of standard deviations above or below the mean in a normal distribution. d. True. In a normal distribution, any percentile less than the 50th corresponds to a negative z-score. e. True. A standard normal distribution has a mean of 0 and a standard deviation of 1.
Step-by-step explanation:
a. False. In a normal distribution, the percentage of scores greater than a specific z-score can be found using a standard normal distribution table. For a z-score of 1.2, the percentage of scores greater than it would be 1 - the cumulative probability up to 1.2. However, the exact value of this percentage cannot be determined without the use of a table or calculator.
b. True. The percentile rank for the mean in any normal distribution is always 50%. This is because the mean divides the distribution into two equal halves.
c. True. A z-score represents the number of standard deviations above or below the mean in a normal distribution. It standardizes raw scores and allows for comparison across different distributions.
d. True. In a normal distribution, any percentile less than the 50th corresponds to a negative z-score. Percentiles below the mean have negative z-scores, while percentiles above the mean have positive z-scores.
e. True. A standard normal distribution has a mean of 0 and a standard deviation of 1. It is represented by the notation Z ~ N(0, 1).