Question

In: Statistics and Probability

In recent years, the total scores for a certain standardized test were normally distributed, with a...

In recent years, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.3 Answer parts A-D below. Round to four decimal places as needed.

  1. Find the probability that a randomly selected medical student who took the test has a total score that was less than 493.

The probability that randomly selected medical student who took the test had a total score that was less than 493 is [____]

  1. Find the probability that a randomly selected medical student who took the test had a total score that was between 495 and 508.

The probability that a randomly selected medical student who took the test had a total score that was between 495 and 508 is [____]

  1. Find the probability that a randomly selected medical student who took the test had a total score that was more than 527.

The probability that a randomly selected medical student who took the test had a total score that was more than 527 is [______]

  1. Identify any unusual events. Explain your reasoning. Choose the correct answer below.

    1. The events in parts A and B are unusual because their probabilities are less than 0.05

    2. None of the events are unusual because all the probabilities are greater than 0.05

    3. The event in part A is unusual because its probability is less than 0.05

    4. The event in part C is unusual because its probability is less than 0.05

Solutions

Expert Solution

Solution:

We are given:

Find the probability that a randomly selected medical student who took the test has a total score that was less than 493.

Answer: We have to find here:

Using the z-score formula, we have:

Find the probability that a randomly selected medical student who took the test had a total score that was between 495 and 508.

Answer: We have to find here

Using the z-score formula, we have:

Find the probability that a randomly selected medical student who took the test had a total score that was more than 527.

Answer: We have to find

Using the z-score formula. we have:

Identify any unusual events. Explain your reasoning. Choose the correct answer below.

Answer: The event in part C is unusual because its probability is less than 0.05

orchestra answered 2 years ago
Next > < Previous

Related Solutions

In a recent​ year, the total scores for a certain standardized test were normally​ distributed, with...
In a recent​ year, the total scores for a certain standardized test were normally​ distributed, with a mean of 500 and a standard deviation of 10.5. Answer parts ​(a)dash​(d) below. ​(a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 489. The probability that a randomly selected medical student who took the test had a total score that was less than 489 is . 1474. ​(Round to four...
For a certain standardized placement test, it was found that the scores were normally distributed, with...
For a certain standardized placement test, it was found that the scores were normally distributed, with a mean of 190 and a standard deviation of 30. Suppose that this test is given to 1000 students. (Recall that 34% of z-scores lie between 0 and 1, 13.5% lie between 1 and 2, and 2.5% are greater than 2.) (a) How many are expected to make scores between 160 and 220? (b) How many are expected to score above 250? (c) What...
A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was...
A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 21.4 and the standard deviation was 5.4. The test scores of four students selected at random are 15​, 22​, 9​, and 36. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 15 is:
A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was...
A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 1507 and the standard deviation was 315. The test scores of four students selected at random are 1900​, 1260​, 2220​, and 1390. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual. The​ z-score for 1900 is nothing. ​(Round to two decimal places as​ needed.) The​ z-score for 1260 is nothing. ​(Round to two decimal places as​...
The scores on a standardized test are normally distributed with a mean of 95 and standard...
The scores on a standardized test are normally distributed with a mean of 95 and standard deviation of 20. What test score is 0.5 standard deviations above the mean?
Scores of a standardized test are approximately normally distributed with a mean of 85 and a...
Scores of a standardized test are approximately normally distributed with a mean of 85 and a standard deviation of 5.5. (a) What proportion of the scores is above 90? (b) What is the 25th percentile of the scores? (c) If a score is 94, what percentile is it on?
Suppose that the scores on a statewide standardized test are normally distributed with a mean of...
Suppose that the scores on a statewide standardized test are normally distributed with a mean of 75 and a standard deviation of 2. Estimate the percentage of scores that were (a) between 73 and 77. % (b) above 79. % (c) below 73. % (d) between 69 and 79. %
Scores for a common standardized college aptitude test are normally distributed with a mean of 481...
Scores for a common standardized college aptitude test are normally distributed with a mean of 481 and a standard deviation of 108. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect. If 1 of the men is randomly selected, find the probability that his score is at least 537.1. P(X > 537.1) = Enter your answer as a number accurate to 4 decimal places. NOTE:...
Scores for a common standardized college aptitude test are normally distributed with a mean of 512...
Scores for a common standardized college aptitude test are normally distributed with a mean of 512 and a standard deviation of 111. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect. If 1 of the men is randomly selected, find the probability that his score is at least 591.7. P(X > 591.7) = Enter your answer as a number accurate to 4 decimal places. If...
Scores for a common standardized college aptitude test are normally distributed with a mean of 514...
Scores for a common standardized college aptitude test are normally distributed with a mean of 514 and a standard deviation of 97. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect. If 1 of the men is randomly selected, find the probability that his score is at least 555.2. P(X > 555.2) = Enter your answer as a number accurate to 4 decimal places. NOTE:...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT