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.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.