Question

SAT scores in one state is normally distributed with a mean of 1571 and a standard deviation of 40. Suppose we randomly pick 40 SAT scores from that state. a) Find the probability that one of the scores in the sample is less than 1588. P(X<1588)=

Answer 1

The probability that one of the scores in the sample is less than 1588 is approximately 0.6645.

Step-by-step explanation:

To find the probability that one of the scores in the sample is less than 1588, we need to calculate the z-score for 1588 using the formula z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation.

Given that the mean is 1571 and the standard deviation is 40, the z-score is (1588 - 1571) / 40 = 0.425.

Using a standard normal distribution table or a calculator, we can find that the probability of a z-score less than 0.425 is approximately 0.6645. Therefore, the probability that one of the scores in the sample is less than 1588 is approximately 0.6645.