Question

Marvel Studio's motion picture Guardians of the Galaxy opened over the first two days of the 2014 Labor Day weekend to a record-breaking $94.3 million in ticket sales revenue in North America. The ticket sales revenue in dollars for a sample of 30 theaters are contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.

	A	B	C	D	E	F
1	Revenue					Formula Used
2	32,050		Sample Size	30		=COUNT(A2:A31)
3	20,870
4	23,290		Point Estimate of Mean (to the whole number	23,104		=AVERAGE(A2:A31)
5	26,370
6	25,675		Standard Deviation (2 decimals)	3974.31		=STDEV.S(A2:A31)
7	20,685
8	22,640		Confidence Coefficient	.99
9	19,800
10	18,720		Level of Significance	?????
11	16,740
12	21,750		Margin of Error (to the whole number	?????
13	24,790
14	25,530		C.I. Lower Limit (to the whole number)	?????
15	26,480		C.I. Upper Limit (to the whole number)
16	25,180
17	21,240		Movie Ticket Price	8.14
18	33,930
19	13,710		Mean Number of Customers per Theater (to the whole number)	?????
20	23,800
21	22,410		Number of Theaters	4060
22	19,940
23	21,170		Total Number of Customers	?????
24	23.920
25	25,490		Total Box Office Ticket Sales (to the whole million)	?????
26	22,230
27	23,730
28	25,950
29	21,820
30	23,270
31	19,760

a. What is the 99% confidence interval estimate for the mean ticket sales revenue per theater (to the nearest dollar)?

($________,$__________)

b. Using the movie ticket price of $8.14 per ticket, what is the estimate of the mean number of customers per theater?

________ customers

c. The movie was shown in 4060 theaters. Estimate the total number of customers who saw Guardians of the Galaxy and the total box office ticket sales for the weekend.

_________ customers

__________ million (to whole number)

Answer 1

Hello Sir/Mam

a) Confidence Interval

Using the values:

Level of significance = 1 - Confidence Level = 1 - 0.99 = 0.01

Standard Deviation = 3974.31

n = Sample Size = 30

Mean = 23104,

Use the following excel formula : "=23104-CONFIDENCE.NORM(0.01,3974.31,30)"

Lower Interval Limit: $21235

Use the following excel formula : "=23104+CONFIDENCE.NORM(0.01,3974.31,30)"

Upper Interval Limit: $24973

Hence, confidence interval is ($21235 , $24973)

b) Mean number of customers per theatre

c) Mean number of customers = 2838

Total number of theaters = 4060

Hence, total number of customers = 2838 * 4060 = 11,522,280customers

Total box office ticket sales = 11,522,280customers * $8.14 $94million

I hope this solves your doubt.

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