Question

The average adult gets 7.45 hours of sleep each night, with a standard deviation of 0.65 hours. A pharmaceutical company developing a sleep aid is researching how much sleep the top 1% of adults get each night, on average. Use a calculator to find how many hours of sleep must an adult get each night to be in the top 1% if the company is only basing their initial research on the sleep habits of 30 adults.

Answer 1

We can use central limit theorem to calculate the distribution of avg. sleeps hours of adults.

Let 'X' represent the sleep hours of adults

Central limit theorem states that

Here we have 30 adults therefore n = 30

We want to find the sleep hours that gets in top 1%. So we have the probability we need to find the 'x'. It says in top 1%. So the sleep hours should be 'x' or more than 'x' to get in top 1%.

We use the normal percentage tables to calculate the z-score from p = 1%. In the tables the values are for more than probabilities so we keep the same inequality sign.

On avg each individual should get 15.732 hrs to be in top 1%.