Question

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

Answer 1

Answer:

The age of an attendee with a z-score of -1.3 would be 19.8 years.

Step-by-step explanation:

Mean age of people at concert = μ = 24

Standard Deviation = σ = 3.2

The ages of people at concert are Normally Distributed, so we can use z-distribution to model the age of the people.

We are given that the z-score of an attendee at the concert is -1.3, we have to find the actual age of the attendee.  We can convert this z-score to the actual age by using the z-score formula. The formula to calculate the z score is:

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

Here, x represents the actual age of the attendee. Substituting the given values, we get:

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

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