A new restaurant with 134 seats is being planned. Studies show that 62% of the customers demand a smoke-free area. How many seats should be in the non-smoking area in order to be very sure (mu plus 3 sigma) of having enough seating there?

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JeanaShupp JeanaShupp · Answer 1 · 2019-08-14T05:38:57+02:00

Answer: 100

Step-by-step explanation:

Given : The total number of seats planned in new restaurant =134

The percentage of customers demand a smoke-free area = 62%

It can also be written as [tex]62\%=\dfrac{62}{100}=0.62[/tex]

The mean of this binomial distribution will be :-

[tex]\mu=np\\\\\mu=(134)(0.62)=83.08[/tex]

Standard deviation:-

[tex]\sigma=\sqrt{np(1-p)}\\\\\Rightarrow\sigma=\sqrt{134(0.62)(0.38)}\approx5.6[/tex]

Now, the number of seats should be in the non-smoking area in order to be very sure of having enough seating there :-

[tex]\mu+3\sigma=83.08+3(5.6)=99.88\approx100[/tex]