A research drone measures the atmospheric pressure at a specific altitude. The pressure $P$ , in suitable units, is modeled as a continuous random variable having a uniform distribution on the interval $[α−3,α+9][\alpha - 3, \alpha + 9]$ , where $α\alpha$ is a constant relating to the specific layer of the atmosphere. A random sample of $n$ independent observations of $P$ is collected, where $n$ is large.

Apply the Central Limit Theorem to find an approximate distribution for the sample mean $Pˉ\bar{P}$ . Give your answer in terms of $n$ and $α\alpha$ where appropriate.

The $n$ observations have a sample mean of $85.5$ . Given that the upper limit of the $98%98\%$ confidence interval for $α\alpha$ is $82.7326$ ,

calculate the value of $n$ . Show your working clearly.

Apply the Central Limit Theorem to find an approximate distribution for the sample mean $Pˉ\bar{P}$ . Give your answer in terms of $n$ and $α\alpha$ where appropriate.

The $n$ observations have a sample mean of $85.5$ . Given that the upper limit of the $98%98\%$ confidence interval for $α\alpha$ is $82.7326$ ,

calculate the value of $n$ . Show your working clearly.

3.7 Hypothesis Testing with the Normal Distribution

Question 50

Markscheme

3.7 Hypothesis Testing with the Normal Distribution

Question 50

Markscheme

3.7 Hypothesis Testing with the Normal Distribution

Question 50

3.7 Hypothesis Testing with the Normal Distribution Questions

3.7 Hypothesis Testing with the Normal Distribution

Question 50

3.7 Hypothesis Testing with the Normal Distribution Questions