Petal Length in Centimeters forIris setosa

1.4	1.4	1.3	1.5	1.4
1.7	1.4	1.5	1.4	1.5
1.5	1.6	1.4	1.1	1.2
1.5	1.3	1.4	1.7	1.5
1.7	1.5	1	1.7	1.9
1.6	1.6	1.5	1.4	1.6
1.6	1.5	1.5	1.4	1.5
1.2	1.3	1.4	1.3	1.5
1.3	1.3	1.3	1.6	1.9
1.4	1.6	1.4	1.5	1.4

Let xbe a random variable representing petal length. Using a TI-84Plus/TI-83Plus/TI-nspire calculator, it was found that the sample mean is 1.46(cm) and the sample standard deviation is 0.17 cm.

a. Examine the histogram for petal lengths. Would you say that the distribution is approximately mound-shaped and symmetric?

Our sample has only 50irises; if many thousands of irises had been used, do you think the distribution would look even more like a normal curve?

b. Use the empirical rule with a sample mean of 1.5 and standard deviation of 0.2to get an interval into which approximately 68%of the petal lengths will fall. Repeat this for 95% and 99.7%.

c. Compute the probability that a petal length is between 1.3and1.6 cm. Compute the probability that a petal length is greater than 1.6 cm.