Methods2024 NHT Exam 1 · Q5Tech-free4 marks

Sample proportion of germinating seeds

In a nursery, $90\%$ of the seeds will grow into seedlings. Let $\hat{P}$ be the random variable representing the sample proportion of seeds that will grow into seedlings for samples of size $100$ .

Find the mean and standard deviation of $\hat{P}$ .

2 marks

Hints, answer checking and worked solutions come with a Season Pass.

Let $Z$ be the standard normal random variable such that $Z \sim N(0, 1)$ and $\Pr(Z > -1) \approx 0.84$ .

Using a normal approximation of $\hat{P}$ , estimate the probability that in a sample of 100, more than $93$ seeds will grow into seedlings. Give your answer correct to two decimal places.

2 marks

Hints, answer checking and worked solutions come with a Season Pass.