Focus groups of 15 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number

Question

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Focus groups of 15 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number

(per group) who recognize the Yummy brand name is 12.5, and the standard deviation is 0.58. Would it be unusual to randomly select 15 people and find that fewer than 9 recognize the Yummy brand name?

Mathematics

1 answer:

babunello [11.8K] · Answer 1 · 2026-04-07T04:19:17+03:00

Answer:

Indeed, having 15 people recognize the brand would be considered unusual, as it lies beyond 2 standard deviations from the average.

Step-by-step explanation:

Examine the provided data.

The average recognition rate for the Yummy brand name among groups is 12.5, with a standard deviation of 0.58.

Mean = μ= 12.5

σ = 0.58

n = 15

$\mu\pm2\sigma=12.5\pm 2(0.58)\\\mu\pm2\sigma=12.5\pm1.16\\\mu\pm2\sigma=[11.34, 13.66]$

Thus, having 15 people recognize the brand would indeed be unusual, as it is outside of the 2 standard deviations from the mean.