Scores for men on the verbal portion of the SAT-1 test are normally distributed with a mean of 509 and a standard deviation of 112. If a man is randomly selected, find the probablity that his score is at least 571
http://davidmlane.com/hyperstat/z_table.html
2.85
To find the probability that a man's score is at least 571 on the verbal portion of the SAT-1 test, we need to use the concept of the standard normal distribution.
The standard normal distribution has a mean of 0 and a standard deviation of 1. To convert the given data to the standard normal distribution, we use the formula:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
In this case, we want to find the probability that a man's score is at least 571, so we need to convert 571 to a z-score. Plugging the given values into the formula:
z = (571 - 509) / 112
z = 62 / 112
z ≈ 0.554
Now, we need to find the probability associated with this z-score using a standard normal distribution table or a statistical calculator. The probability is the area under the curve to the right of the z-score.
Looking up the z-score of 0.554 in the standard normal distribution table, we find that the corresponding probability is approximately 0.2912.
Therefore, the probability that a randomly selected man's score is at least 571 on the verbal portion of the SAT-1 test is approximately 0.2912 or 29.12%.