QUESTION 1

1. It is believed that the mean value of a variable measured for an entire population of individuals has value = 37 and that for the population the standard deviation is ? = 8.57. A sample of size n= 83 is to be taken from the population. According to the central limit theorem, the sampling distribution of the mean is

Which one:

Normal( 37 , 8.57²)

Normal( 83 , 0.94²)

Normal( 83 , 8.57²)

Normal( 37 , 0.94²)

QUESTION 2

A website claims to offer up to date information on the distribution of the price of petrol per litre offered by service stations in Ireland.

On one particular day the website claims that the average price of petrol per litre offered is = 1.32 euro and that prices vary between petrol stations by a standard deviation of ? = 0.07 euro.

Suppose a consumer group decides to check the website's claim by sampling n = 47 petrol stations in Ireland and recording the price per litre that day for these petrol stations.

Answer the following questions :

Question 1 :Assuming the claim is true, the sampling distribution of the mean is :

a: Normal( 1.32 , 0.01²)

b: Normal( 47 , 0.01²)

c: Normal( 47 , 0.07²)

d: Normal( 1.32 , 0.07²)

Insert your choice( a /b /c /d ):

Question 2:The mean price of petrol from the sample was recorded to be 1.312. Assuming the website's claim is true calculate how likely it was that the sample gave a mean price of 1.312 or less :.(4 decimal places)

Question 3

The daily revenue at a university snack bar has been recorded for the past five years. Records indicate that the mean daily revenue is = 5760 euro and vary between days by a standard deviation of ? = 500 euro. The distribution is skewed to the right due to several high volume days (football game days).

Suppose a sample of n = 500 days are randomly selected and the sample average daily revenue computed.

Answer the following questions :

Question 1 :The sampling distribution of the mean is :

a: Normal( 5760 , 22.36²)

b: Normal( 500 , 500²)

c: Normal( 5760 , 500²)

d: Normal( 500 , 22.36²)

Insert your choice( a /b /c /d ):

Question 2:The sample average daily revenue was recorded to be 5783. Calculate how likely it was that the sample gave an average daily revenuegreater than or equalto 5783 :.(4 decimal places)

QUESTION 4

The last question stated "The distribution is skewed to the right due to several high volume days (football game days)". Based on this statement do you have any reservations about the reliability of the probability you calculated in the last question ?

a.Yes- The distribution of revenue for all days, i.e. the population distribution is skewed, not symmetric and therefore the population does not follow the normal distribution. Therefore the sampling distribution of the mean does not follow the normal distribution.

b.No- The distribution of revenue for all days, i.e. the population distribution, is skewed, not symmetric and therefore the population does not follow the normal distribution. However theCentral Limit Theorem applies in this case, and the sampling distribution of the mean follows a normal distribution even if the population does not have a normal distribution.

c.Yes- The distribution of revenue for all days, i.e. the population distribution is skewed, not symmetric and therefore the population does not follow the normal distribution. Therefore the assumption required to carry out the analysis, that the population be normally distributed,is not valid.

Question 5

?

The Central Limit Theorem states that If a random sample of size n observations is selected from a population in which the variable of interest, X, has mean u and standard deviation o, then the sampling distribution of the mean, X , will be O a. approximately normal with a mean of /7 = f and a standard deviation of = o/vn and the population from which we are sampling can have any shape, X ~ anyshape. Ob. approximately normal with a mean of / = 7 and a standard deviation of = o/vn and the population from which we are sampling can have any shape, X - anyshape. O c. approximately normal with a mean of /7 = / and a standard deviation of = o and the population from which we are sampling must be normally distributed X ~ N(.o). O d. approximately normal with a mean of //y = / and a standard deviation of = o/vn and the population from which we are sampling must be normally distributed X ~ N(4,5)