Question

Best Western Gift shop is interested to know how much money, on average, their customers spend each visit in the housewares department. They go back through their records and draw a sample of 1,000 and calculate each customer’s average spending on housewares.

a) Identify the population, sample, parameter, statistic, variable and data for this example.

b) Describe a situation in which you would calculate a parameter rather than a statistic.

Best Western determined that each customer’s spending is normally distributed with a mean of $37 and a standard deviation of $3.40.

c) What percentage of people spend between $20 and $32?

d) Customers get a $6 coupon when they spend over $35. Of the next 200 people that visit the store, how many coupons can they expect to give away?

Answer 1

a ) Population : All the people who visit in the housewares department, listed in the records is the population.

Sample : 1000 people who visit in the housewares department, selected from the records is the sample.

parameter : population mean that is the average speand of money from all the peoples who visit in the housewares department in the records.

statistic : Sample mean that is the average speand of money from the peoples who visit in the housewares department in the records.

Variable : Money spend in by the people who visit in the housewares department.

Data : List of money spend by each people the the data for this example

b) Describe a situation in which you would calculate a parameter rather than a statistic.

If the poppulation is finite and small then we would find parameter by taking all the element in the population.

Also if the error is more serious in nature then we would study whole population and calculate parameters.

If we have a time and money is not a problem then we go through complete enumeration of the population rather than the sample and calculate parameters.

In this example, if we take all the people who visit in the housewares department in the records then it is called complete enumeration and the mean of the money spend by the people is called parameter.

Best Western determined that each customer’s spending is normally distributed with a mean of $37 and a standard deviation of $3.40.

Let X be the random variable which takes the value of money spend by the people who visit in the housewares department then X follows normal distribution with mean = $37 and standard deviation of $3.40..

Mathematically , X ~ N ( = 37, = 3.40 )

c) We want to find P( 20 < X < 32 ) = P( X < 32 ) - P( X < 20 ) ------(1)

Let's use excel:

P( X < 32 ) = "=NORMDIST(32,37,3.4,1)" = 0.0707

P(X < 20) = "=NORMDIST(20,37,3.4,1)" = 0

Plug these values in equation (1) , we get :

P( 20 < X < 32 = 0.0707 - 0 = 0.0707

d) First we need to find P( X > 35 ) = 1 - P(X < 35 ) ------( 2 )

P(X < 35 ) = "=NORMDIST(35,37,3.4,1)" = 0.2782

Plug this value in equation ( 2 ), we get

P( X > 35 ) = 0.7218

So that the next 200 people that visit the store 200*0.7218 = 144.36 which is approximately equal to 144 coupon, can they expect to give away.