As we study random variables, the idea of z-scores will come up again. What is a z-score (in words) and what is the formula for
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Answer:
22.29% probability that both of them scored above a 1520
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 problem, we have that:
The first step to solve the question is find the probability that a student has of scoring above 1520, which is 1 subtracted by the pvalue of Z when X = 1520.
So
has a pvalue of 0.5279
1 - 0.5279 = 0.4721
Each students has a 0.4721 probability of scoring above 1520.
What is the probability that both of them scored above a 1520?
Each students has a 0.4721 probability of scoring above 1520. So
22.29% probability that both of them scored above a 1520