Question

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?

Answer 1

Answer: 100

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
`62\%=(62)/(100)=0.62`

The mean of this binomial distribution will be :-

`\mu=np\\\\\mu=(134)(0.62)=83.08`

Standard deviation:-

`\sigma=√(np(1-p))\\\\\Rightarrow\sigma=√(134(0.62)(0.38))\approx5.6`

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

`\mu+3\sigma=83.08+3(5.6)=99.88\approx100`