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Answer:
16 women ran faster than Joan
Step-by-step explanation:
The z-score measures how many standard deviations a score X is above or below the mean.
Each z-score has its respective p-value, which is the percentile of X. We find the p-value looking at the z-table.
Joan’s finishing time for the Bolder Boulder 10K race was 1.74 standard deviations faster than the women’s average for her age group.
So [tex]Z = 1.74[/tex]
[tex]Z = 1.74[/tex] has a pvalue of 0.9591. Which means that Joan was faster than 95.91% of the participants and slower than 100-95.91 = 4.09% of the participants.
Assuming a normal distribution, how many women ran faster than Joan?
380 participants
4.09% faster than Joan
0.0409*380 = 15.5
Rounding up, 16 women ran faster than Joan
The standard deviation is the average amount of variability in our data set. It tell about how far each score lies from the mean.
16 women ran faster than Joan
- A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
- Z-score is measured in terms of standard deviations from the mean.
- If a Z-score is 0, it indicates that the data point's score is identical to the mean score.
- The z-score measures how many standard deviations a score X is above or below the mean.
- Each z-score has its respective p-value, We find out p - values from z- table.
Since, Joan’s finishing time for the Bolder Boulder 10K race was 1.74 standard deviations faster than the women’s average for her age group.
So, Z - score = 1.74
From z - table, we saw that for Z = 1.74 , corresponding p-value is 0.9591. It means that Joan was faster than 95.91% of the participants and slower than 100-95.91 = 4.09% of the participants.
Since, There were 380 women who ran in her age group.
we computed that, 4.09% faster than Joan
Number of women run faster than Joan is, = [tex]380*\frac{4.09}{100}=15.542[/tex] , nearly = 16
Thus, 16 women ran faster than Joan
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