As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a...

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As a special promotion for its 20-ounce bottles of soda, a softdrink company printed a message on the inside of each cap. Some ofthe caps said, â€œPlease try again,â€ while others said, â€œYouâ€™re awinner!â€ The company advertised the promotion with the slogan â€œ1 in6 wins a prize.â€ Suppose the company is telling the truth and thatevery 20-ounce bottle of soda it fills has a 1-in-6 chance of beinga winner. Seven friends each buy one 20-ounce bottle of the soda ata local convenience store. Let X = the number who win a prize. Theprobability distribution of X is shown here.
a)The store clerk is surprised when 3 of the friends win aprize. Is this group of friends just lucky, or is the companyâ€™s1-in-6 claim inaccurate? Find the probability that at least 3 of agroup of 7 friends would win a prize and use the result to justifyyour answer.
Winners
0
1
2
3
4
5
6
7
Probability
0.2791
0.3907
0.2344
0.0781
0.0156
0.0019
0.0001
0.000004

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4.5 Ratings (901 Votes)

The given distribution of X is Winners01234567Probability027910390702344007810015600019000010000004So to test the companies claim we will find the expected numberof winners in a group of 7 See Answer

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Winners	0	1	2	3	4	5	6	7
Probability	0.2791	0.3907	0.2344	0.0781	0.0156	0.0019	0.0001	0.000004