A group of 266 persons consist of men, women, and children. There are four times as many men as children. And twice as many wome
1 answer:
There are 152 men, 76 women and 38 children.
Step-by-step explanation:
Total persons = 266
Let,
men = m
women = w
children = c
According to given statement;
m+w+c=266 Eqn 1
m = 4c Eqn 2
w = 2c Eqn 3
Putting value of m and w from Eqn 2 and 3 in Eqn 1
Dividing both sides by 7
Putting c=38 in Eqn 2;
Putting c=38 in Eqn 1;
There are 152 men, 76 women and 38 children.
Keywords: linear equations, substitution method
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Answer:
The actual SAT score is 2024.
The equivalent ACT score is 29.49.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
SAT score that is in the 95th percentile
Scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312, which means that
95th percentile is X when Z has a pvalue of 0.95, so X when Z = 1.645. The score is:
The actual SAT score is 2024.
Equivalent ACT score:
The equivalent ACT score is the 95th percentile of ACT scores.
Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1, which means that . So
The equivalent ACT score is 29.49.