The ages of people at a concert are normally distributed with a mean of 24 years and a standard deviation of 3.2 years.
1 answer:
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:
In this case, x represents the actual age of the attendee. Substituting the known values gives us:
Thus, the age of an attendee with a z-score of -1.3 would indeed be 19.8 years.
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Begin by disregarding the inequality symbol and substituting it with an '=' sign. After that, determine the x- and y-intercepts.
15x + 10y = 1,100
x-intercept:
15x + 0 = 1,100
x = 1,100/15 = 73.33
y-intercept:
0 + 10y = 1,100
y = 1,100/10 = 110
Now, plot the points (73.33,0) and (0,110). Given that the inequality symbol is ≥, representing equality, connect these points using a solid line.
Next, let's identify a point on the graph, for instance, the origin (0,0). Use this point in the equation.
15x + 10y ≥ 1,100
15(0) + 10(0)? 1,100
0? 1,100
0 < 1,100
This makes the ≥ statement false. As a result, the alternate area defined by the line is the solution. Consequently, shade that region. The resulting graph is displayed in the attached image.
