Question

A new restaurant with 138 seats is being planned. Studies show that 59​% 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?

Answer 1

Explanation:

Given that a new restaurant with 138 seats is being planned. Studies show that 59​% of the customers demand a​ smoke-free area.

Non smoke area = 100-59=41%

mu for non smoke area = 0.41

Std deviation =
`\sqrt{(pq)/(n) } =0.0418`

mu-3sigma =
`0.41-3(0.0418) =0.2843`

mu+3 sigma =
`0.41+3(0.0418)=0.5354`

Thus 28.43 to 53.54 percent should be in non smoke area

Or 39.2334 to 73.8852 seats

74 seats should be in the​ non-smoking area in order to be very sure ​(mu plus 3 sigma​) of having enough seating​ there