Question

Focus groups of 11 people are randomly selected to discuss products of the Famous Company. It is determined that the mean number (per group) who recognize the Famous brand name is 6.2, and the standard deviation is 0.51. Would it be unusual to randomly select 11 people and find that greater than 9 recognize the Famous brand name?

Answer 1

Answer: It would not be unusual to randomly select 11 people and find that greater than 9 recognize the famous brand name.

Explanation:

Since we have given that

Mean = 6.2

Standard deviation = 0.51

Average number of people = 11

So, using the normal distribution, we get that

`z=(9-11)/(0.51)=(-2)/(0.51)=-3.921`

Now, we will check that

`P(\bar{X}>9)=P(z>-3.921)=1-0.00004=0.99996`

Hence, It would not be unusual to randomly select 11 people and find that greater than 9 recognize the famous brand name.