Question 2.(4 points) A manager of a restaurant in a commercial building would like to offer a new tea drink to customers. She randomly polled 100 customers and asked how many of them drink tea on a regular basis. Of the 100 customers, 41 reported to be tea drinkers.
a) (1 point) Calculate p̂, the estimate of the true population proportion of customers who drink tea.
b) (3 points) Before the poll was conducted, the manager believed that 52% of customers were tea drinkers. Assuming this assertion is true, find P(p̂ ≤ 0.41).
Question 3. (6 Points) The inorganic mercury content in a single cigarette of a particular brand is a random variable with mean 25 ng and a population standard deviation of 12 ng. A random sample of n = 100 cigarettes is taken for analysis.
(2 points) What is the approximate distribution of the sample mean X ?
b) (2 points) The inorganic mercury content for a cigarette is considered high when the content is greater than 29 ng. What is the probability that the resulting sample mean content will be greater than 29 ng?
c) (2 points) Now suppose that the market analyst would like to test another brand of cigarettes and selects a random sample of n = 25 cigarettes from a population with mean inorganic mercury content 25 ng, but the standard deviation is now estimated from the sample as 10 ng. What is the probability that the sample mean content will be greater than 29 mg for this brand?