1. Find the following probabilities for the standard normal random variable z. (Round your answers to four decimal places.)

(a) P(1.42 < z < 0.66) =

(b) P(0.51 < z < 1.79) =

(c) P(1.53 < z < 0.46) =

(d) P(z > 1.34) =

(e) P(z < 4.39) =

2. Calculate the area under the standard normal curve to the left of these values. (Round your answers to four decimal places.)

(a) z = 1.1

(b) z = 1.87

(c) z = 0.90

(d) z = 4.13

3. (a) Find a z₀ that has area 0.9382 to its left. (Round your answer to two decimal places.) z₀ =

(b) Find a z₀ that has area 0.05 to its left. (Round your answer to two decimal places.)

z₀ =

4. An experimenter publishing in the Annals of Botany investigated whether the stem diameters of the dicot sunflower would change depending on whether the plant was left to sway freely in the wind or was artificially supported. Suppose that the unsupported stem diameters at the base of a particular species of sunflower plant have a normal distribution with an average diameter of 35 millimetres (mm) and a standard deviation of 3 mm.

(a) What is the probability that a sunflower plant will have a stem diameter of more than 40 mm? (Round your answer to four decimal places.) (b) If two sunflower plants are randomly selected, what is the probability that both plants will have a stem diameter of more than 40 mm? (Round your answer to four decimal places.) (c) Within what limits would you expect the stem diameters to lie, with probability 0.95? (Round your answers to two decimal places.)

lower limit	mm
upper limit	mm

(d) What diameter represents the 80th percentile of the distribution of diameters? (Round your answer to two decimal places.) mm