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shutvik
2 months ago
11

The ages of people at a concert are normally distributed with a mean of 24 years and a standard deviation of 3.2 years.

Mathematics
1 answer:
Leona [12.6K]2 months ago
3 0

Response:

An attendee with a z-score of -1.3 would have an age of 19.8 years.

Detailed explanation:

Average age at the concert = μ = 24

Standard Deviation = σ = 3.2

Ages of concert attendees are Normally Distributed, allowing us to utilize z-distribution for modeling the attendees' ages.

Given the z-score of -1.3 for a concert attendee, we need to find the actual age. We can convert this z-score to real age by employing the z-score formula. The formula for calculating the z-score is:

z=\frac{x-\mu}{\sigma}

In this case, x represents the actual age of the attendee. Substituting the known values gives us:

-1.3=\frac{x-24}{3.2} \\\\ -1.3 \times 3.2 =x-24\\\\ -4.16=x-24\\\\ -4.16+24=x\\\\ x=19.8\\

Thus, the age of an attendee with a z-score of -1.3 would indeed be 19.8 years.

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