Question

Thuy Dau, Ngoc Bui, Sam Su, and Lan Voung conducted a survey as to how long customers at a clothing store claimed to wait in the checkout line until their turn. Let X = time in line. Below are the ordered real data (in minutes).

0.50	3.00	4.75	6.00	7.50
1.50	3.25	4.75	6.00	7.75
1.75	3.25	5.00	6.25	8.00
1.75	3.50	5.00	6.50	8.25
1.75	4.00	5.00	6.75	8.50
1.75	4.00	5.25	6.75	8.50
2.00	4.00	5.50	6.75	9.00
2.00	4.00	5.50	6.75	9.00
2.75	4.50	5.50	6.75	9.75
3.00	4.50	5.75	7.00	10.75

Part (a)

Calculate the sample mean x and the sample standard deviation s. (Round your answers to two decimal places.)

x	=	min
s	=	min

Part (b)

Construct a histogram.

Part (c)

In words, describe the shape of your histogram.

Part (d)

Let the sample mean approximate μ and the sample standard deviation approximate σ.The distribution of X can then be approximated by X ~  

  

Part (e)

Use the distribution in part (d) to calculate the probability that a person will wait fewer than 6.2 minutes. (Round your answer to four decimal places.)

Part (f)

Determine the cumulative relative frequency for waiting less than 6.2 minutes. (Round your answer to two decimal places.)

Part (g)

Why aren't the answers to parts (e) and (f) exactly the same?

Part (h)

Why are the answers to parts (e) and (f) as close as they are?

Part (i)

If only 10 customers were surveyed instead of 50, do you think the answers to parts (e) and (f) would have been closer together or farther apart?

closer together farther apart    

.

Answer 1

a.) Mean X = 5.23 min

Standard Deviation X = 2.43 min

b.)

Bin Frequenc 0.50 1.96 3.43 4.89 6.36 7.82 9.29 11.00 Histogram 12 10 More 0 Frequency 0.50 1.96 3.43 4.896.36 7.82 9.29 11.00 More Bin

c.) The histogram is close to the bell curve i.e the normal curve

d.) So the distribution of X can be approximated as, X ~ N(5.23 , 2.43) i.e Normal with mean 5.23 and standard deviation 2.43