Question

1. which of these is most likely to form a normal distribution according to the law of large numbers? a 10 dice rolled 1 time c 10 dice rolled 100 times b 10 dice rolled 10 times d 10 dice rolled 1000 times 9. if sat scores for high - school seniors are normally distributed with a mean score of 1500, then a no one will score below 1000. b no one will score over 2000. c everyones score will be the same. d the number of people who score a 1600 will equal the number of people who score a 1400. 10. on a normal distribution, the mean a equals the median. c has a z - score of 0. b equals the mode. d all of the above 11. according to the \68 - 95 - 99.7 rule\ about what % of values are within (+/-) two standard deviations of the mean? a 99.7% b 95% c 68% d 50% 12. which of following is not true of a normal distribution? a it has two tails. c it has an area of 1. b it is symmetrical. d zero is the least possible value for a z - score. 13. to the right is the normal distribution for heights of us adult males. according to the 68 - 95 - 99.7 rule, what height range would 95% of the data fall? a exactly 70.9 inches b 62.6 inches - 79.1 inches c 65.4 inches - 76.4 inches d 68.1 inches - 73.6 inches heights of us adult males heights (in)

Explanation:

Step - by - Step Format

Step1: Recall the Law of Large Numbers for normal distribution

The Law of Large Numbers states that as the number of trials increases, the distribution of outcomes approaches a normal distribution. Rolling 10 dice 1000 times has the largest number of trials among the options.

Step2: Analyze normal - distribution properties for question 9

In a normal distribution with mean $\mu = 1500$, scores above 2000 are possible, scores below 1000 are possible, and scores are not all the same. Since the normal distribution is symmetric about the mean, the number of people who score a 1600 will equal the number of people who score a 1400 (because 1600 - 1500=1500 - 1400).

Step3: Recall normal - distribution central - tendency relationships for question 10

In a normal distribution, the mean = median = mode, and the mean has a z - score of 0.

Step4: Recall the 68 - 95 - 99.7 rule for question 11

The 68 - 95 - 99.7 rule states that about 95% of values are within $\pm2$ standard deviations of the mean.

Step5: Analyze normal - distribution characteristics for question 12

A normal distribution has two tails, is symmetric, and has an area under the curve equal to 1. Zero is not the least possible value for a z - score (z - scores can be negative).

Step6: Use the 68 - 95 - 99.7 rule for question 13

For a normal distribution, 95% of the data lies within $\pm2$ standard deviations of the mean. Looking at the given normal - distribution graph for heights of US adult males, the range is 65.4 inches - 76.4 inches.

Answer:

1. D. 10 dice rolled 1000 times
2. C. The number of people who score a 1600 will equal the number of people who score a 1400
3. D. All of the above
4. B. 95%
5. D. Zero is the least possible value for a z - score
6. C. 65.4 inches - 76.4 inches