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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.
Answer:
9.
Step-by-step explanation:
We have been given that dimensions of original photo are 4 inches by 6 inches. We want the photo on the poster to be of dimensions 3 feet by 4 1/2 feet.
First of all we will convert dimensions of poster from feet to inches.
Now let us compare sides of our original photo with corresponding sides of poster.
Now let us compare the second pair of corresponding sides.
We have seen that sides of poster are 9 times the sides of our original photo, therefore, the scale factor of this dilation is 9.