Let x be a random variable representing petal length.

Mean=1.46

St.dev= 0.17

8. Use the empirical rule with the mean and standard deviation you found in questions 1 and 2 rounded to 2 decimal places, to obtain an interval in which approximately 68% of the petal lengths should fall. Round your answers to two decimal places. [Write your interval in the following form (lower bound, upper bound). For instance, if you got 5.76 & 10.65, then type your answer as (5.76.10.65)]

9. Using the 68% interval found in question above, look at the data set provided and count how many irises fall in the interval. Of the 50 irises sampled, how many irises petal length fell in this interval?

10. Using the answer from above, compute the percentage of irises from the sample (raw data) set fall in 68% interval?

11. Use the empirical rule with the mean and standard deviation you found in questions 1 and 2 rounded to 2 decimal places, to obtain an interval in which approximately 95% of the petal lengths should fall. Round your answers to two decimal places. [Write your interval in the following form (lower bound, upper bound). For instance, if you got 5.76 & 10.65, then type your answer as (5.76.10.65)]

12.Using the 95% interval found in question above, look at the data set provided and count how many irises fall in the interval. Of the 50 irises sampled, how many irises petal length fell in this interval?

13. Using the answer from above, compute the percentage of irises from the sample (raw data) set fall in 95% interval?

14. Use the empirical rule with the mean and standard deviation you found in questions 1 and 2 rounded to 2 decimal places, to obtain an interval in which approximately 99.7% of the petal lengths should fall. Round your answers to two decimal places. [Write your interval in the following form (lower bound, upper bound). For instance, if you got 5.76 & 10.65, then type your answer as (5.76.10.65)]

15. Using the 99.7% interval found in question above, look at the data set provided and count how many irises fall in the interval. Of the 50 irises sampled, how many irises petal length fell in this interval?

16. Using the answer from above, compute the percentage of irises from the sample (raw data) set fall in 99.7% interval?

17.How do your computed percentages based on the sample (raw) data compare with the empirical rule percentages?

18. Compute the probability that a petal length is greater than 1.5cm. Show all work. Include the z score and appropriate probability in your work.

P(x>1.5)= p(z>______)=________

19. Compute the probability that a petal length is less than 1.4cm. Show all work. Include the z score and appropriate probability in your work.

P(x<1.4)= p(z<______)=________

20. Compute the probability that a petal length is between 1.4 and 1.5cm. Show all work.

P(1.4

21. Suppose that a random sample of 30 irises is obtained. Compute the probability that the average petal length for this sample is greater than 1.5cm. Show all work. Include the z score and appropriate probability in your work.

P(xbar>1.5)=

22. Suppose that a random sample of 30 irises is obtained. Compute the probability that the average petal length for this sample is less than 1.4cm. Show all work. Include the z score and appropriate probability in your work.

P(xbar<1.4)=

23. Suppose that a random sample of 30 irises is obtained. Compute the probability that the average petal length for this sample is between 1.4 and 1.5cm. Show all work. P(1.4

24. How are questions 18 & 21different? (note the same could be said about 19 & 22 and 20 & 23) Why do you suppose the answers are so different? Hint they should be different what is the cause?