Sampling after lecture quiz

A college has 300 students in Year One, 280 students in Year Two. Alice wishes to find out how the gaming habits of Year One students, so she sends a questionnaire to the 300 students in Year One. Do these 300 students form a sample or a population?

• Population

• Sample

A random sample of size 100 is taken from a population with mean 30 and standard deviation 5.

(a) Find an approximate value for the probability that the sample mean lies between 29.2 and 30.8. Correct your answer to 3 significance figures.

A random sample of size 100 is taken from a population with mean 30 and standard deviation 5.

(b) Is it necessary to make any assumptions about the distribution of the population?

• Yes

• No

Give a reason for your above answer.

Let X ml be the volume of bottle of apple juice. Which of the following(s) is (are) represents the probability of thrice the volume of a randomly chosen bottle is less than 1000ml?

•  $P\left(X_1+X_2+X_3<1000\right)$  

•  $P\left(3X<1000\right)$  

Let X ml be the volume of bottle of apple juice. Which of the following(s) is (are) represents the probability of the total of the volume of three randomly chosen bottles is less than 1000ml?

•  $P\left(X_1+X_2+X_3<1000\right)$  

•  $P\left(3X<1000\right)$  

Which of the following represent the variance of the total volume of randomly selected 3 bottles?

• $Var\left(X_1+X_2+X_3\right)\$

• $Var\left(3X\right)$

• $3^2Var\left(X\right)$

• $3Var\left(X\right)$

Which of the following (s) represent the variance of thrice the volume of randomly selected bottle?

• $Var\left(X_1+X_2+X_3\right)\$

• $Var\left(3X\right)$

• $3^2Var\left(X\right)$

• $3Var\left(X\right)$