Of the 15-year-olds at a karate school, 5 have black belts and 9 have brown belts. Among the 16-year-olds, 13 have black belts a
1 answer:
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Answer:
a) Kenji's time had a lower z-score, which means that he is better compared to other runners on his level, and better to his peers compared to Nedda.
b) Rachel, because her time had the lowest z-score.
Step-by-step explanation:
Z-score:
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
The lower the time, the better the runner is. So whoever's time has a lower z-score is a better runner. So initially, we find the z-score of each student's time.
An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in the class, ran 1 mile in 8 minutes.
This means that for Rachel's time, we have that . So
A junior high school class ran 1 mile in an average of 9 minutes, with a standard deviation of 2 minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes.
This means that for Kenji's time, we have that . So
A high school class ran 1 mile in an average of 7 minutes with a standard deviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes.
This means that for Nedda's time, we have that . So
(a) Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?
Kenji's time had a lower z-score, which means that he is better compared to other runners on his level, and better to his peers compared to Nedda.
(b) Who is the fastest runner with respect to his or her class? Explain why
Rachel, because her time had the lowest z-score.
Answer:
The estimate of the product is about 35 answer C
Step-by-step explanation:
- We use rounding to estimate the product of two fractions
- The mixed number has whole number and fraction
- To round the mixed number we look to the fraction
- If the numerator is half or greater than half the denominator, then we
add the whole number by 1 and cancel the fraction
- If the numerator is less than half the denominator, then we keep the
whole number as it and cancel the fraction
- Ex: If the mixed number is , 3 is more than
half 4 then we will add 2 by 1 and cancel the fraction part, the
mixed number after rounding is 3
- Ex: If the mixed number is , 1 is less than
half 4 then we will keep 5 as it and cancel the fraction part, the
mixed number after rounding is 5
* Lets solve the problem
∵ In the part 3 is more than half 4
∴ The rounding value of is 5
∵ In the part 2 is less than half 17
∴ The rounding value of is 7
∴
* <em>The estimate of the product is about 35</em>