The height of a certain species of sunflower, in cm, is normally distributed with a mean of 180 cm and a standard deviation of 12 cm. A gardener has one of these sunflowers.
Find the probability that the sunflower is taller than 170 cm.
A sunflower is already 170 cm tall. Find the probability that it grows to be taller than 195 cm.
The gardener believes that the mean height of these sunflowers is greater than 180 cm. He took a random sample of 36 sunflowers and found that their mean height was 183.5 cm. Stating your hypotheses clearly and using a 5% level of significance, test the gardener's belief.
