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bixtya [17]
3 years ago
10

Suppose you can somehow choose two people at random who took the SAT in 2014. A reminder that scores were Normally distributed w

ith mean and stanard deviation of 1497 and 322, respectively. What is the probability that both of them scored above a 1520? Assume that the scores of the two test takers are independent.
Mathematics
1 answer:
Sindrei [870]3 years ago
8 0

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 \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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:

\mu = 1497, \sigma = 322

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

Z = \frac{X - \mu}{\sigma}

Z = \frac{1520 - 1497}{322}

Z = 0.07

Z = 0.07 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

P = 0.4721*0.4721 = 0.2229

22.29% probability that both of them scored above a 1520

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