Question

A hotel chain recently surveyed 300 new customers and asked them to rate their overall satisfaction with their recent hotel stay. The survey estimated a mean satisfaction of 7 with a standard deviation of 1. If the data are normal distributed, approximately how many new customers gave the hotel a rating of 6,7, or 8? 150 175 O 200 285

Answer 1

Answer: 200

Explanation:

Given : A hotel chain recently surveyed 300 new customers and asked them to rate their overall satisfaction with their recent hotel stay.

The survey estimated a mean satisfaction
`\mu=7` with a standard deviation
`\sigma=1`.

Let x represents the rating given by customer.

Using formula ,
`z=(x-\mu)/(\sigma)`.

For x = 6, z= -1

For x= 8 , z=1

The probability that new customers gave the hotel a rating of 6,7, or 8 will be :-

`P(6\leq x\leq8)=P(-1\leq z\leq1)=P(z\leq1)-P(z\leq-1)\\\\=P(z\leq1)-(1-P(z\leq1))\\\\=2P(z\leq1)-1\\\\=2(0.8413447)-1=0.6826894\approx0.68`

The number of new customers gave the hotel a rating of 6,7, or 8 will be :-

`0.68*300=204\approx200` [Rounded to the nearest tens]

Hence, the approximate number of new customers gave the hotel a rating of 6,7, or 8 =200