Respuesta :
Answer:
The proportion of women who ran the marathon and had a finishing time less than Kathy's is 66% (rounding to the next whole)
Explanation:
1. Let's review the information given to us to answer the question properly:
μ of finishing time for women = 259 minutes
σ of finishing time for women = 32 minutes
Finishing time for Kathy = 272 minutes
2. What proportion of women who ran the marathon had a finishing time less than Kathy's? Show your work.
Let's calculate the z-score for the finishing time for Kathy, as follows:
z-score = (272 - 259)/32
z-score = 13/32 = 0.41 (rounding to the next hundredth)
Using the z-table, now we can calculate the proportion of women who ran the marathon had a finishing time less than Kathy's:
p (z=0.41) = 0.6591
The proportion of women who ran the marathon and had a finishing time less than Kathy's is 66% (rounding to the next whole)
The part of women who took part in the marathon and possessed a finishing time lower than Kathy post rounding it off to the next whole number would be:
- 66%
Given that,
The mean of women's finishing time = 259 minutes
The Standard deviation of women's finishing time = 32 minutes
Kathy's finishing time = 272 minutes
To find,
The part of women who took part in the marathon and possessed a finishing time lower than Kathy post rounding it off to the next whole number = ?
We will first determine Kathy's finishing time through z-score,
z-score [tex]= (272 - 259)/32[/tex]
[tex]= 13/32[/tex]
[tex]= 0.41 (after rounding to the next hundredth)[/tex]
By employing the z-table
[tex]p (z)=0.41[/tex]
[tex]= 0.6591[/tex]
Post rounding off to next hundredth [tex]0.6591[/tex] becomes [tex]66[/tex]%
Thus, 66% is the correct answer.
Learn more about 'Percentage' here:
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