Answer:
The inter-decile range of IQ is 40.96.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
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, we have that:
![\mu = 100, \sigma = 16](https://tex.z-dn.net/?f=%5Cmu%20%3D%20100%2C%20%5Csigma%20%3D%2016)
First decile:
100/10 = 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.
![-1.28 = \frac{X - 100}{16}](https://tex.z-dn.net/?f=-1.28%20%3D%20%5Cfrac%7BX%20-%20100%7D%7B16%7D)
![X - 100 = -1.28*16](https://tex.z-dn.net/?f=X%20-%20100%20%3D%20-1.28%2A16)
![X = 79.52](https://tex.z-dn.net/?f=X%20%3D%2079.52)
Ninth decile:
9*(100/10) = 90th percentile, which is X when Z has a pvalue of 0.9. So it is X when Z = 1.28.
![1.28 = \frac{X - 100}{16}](https://tex.z-dn.net/?f=1.28%20%3D%20%5Cfrac%7BX%20-%20100%7D%7B16%7D)
![X - 100 = 1.28*16](https://tex.z-dn.net/?f=X%20-%20100%20%3D%201.28%2A16)
![X = 120.48](https://tex.z-dn.net/?f=X%20%3D%20120.48)
Interdecile range:
120.48 - 79.52 = 40.96
The inter-decile range of IQ is 40.96.
Answer:
5p-q = 5. (-6) - 5 = -30 - 5 = -35
5pq= 5. (-6) . 5 = -30 . 5 = -150
Step-by-step explanation:
Answer: The new ratio will be 1/4
Explanation: The initial ratio of losses to wins is 3 to 2. If we sum the numer of losses and wins 3 + 2 = 5 games, that means they loss 3 out of 5 games , and they win 2 out of 5 games.
So if they had won twice as many of the games, that is 2*2=4. And since the number of games is the same ( 5 ), then they would have won 4 games and loss only 1.
So the new ratio of losses to wins will be 1 to 4, or expressed in a fraction: 1/4
Answer:
![7y = 56](https://tex.z-dn.net/?f=7y%20%3D%2056)
Step-by-step explanation:
![3(y - 1) = 21](https://tex.z-dn.net/?f=3%28y%20-%201%29%20%3D%2021)
Divide 3 on both sides:
![y - 1 = 7](https://tex.z-dn.net/?f=y%20-%201%20%3D%207)
Add 1 to both sides:
![y = 8](https://tex.z-dn.net/?f=y%20%3D%208)
Multiply by 7 on both sides:
![7y = 56](https://tex.z-dn.net/?f=7y%20%3D%2056)