A math teacher gives two different tests to measure students' aptitude for math. Scores on the first test are normally distributed with a mean of 25 and a standard deviation of 4.6. Scores on the second test are normally distributed with a mean of 68 and a standard deviation of 11.9. Assume that the two tests use different scales to measure the same aptitude. If Bill scores 27 on the first test, and Dave scores 71 on the second test, describe their relative performance.
Is there enough information to solve this?
Z = (score - mean)/ standard deviation
Calculate Z scores for both persons.
Just comparing the Z scores will tell you which person did relatively better within their groups.
Yes, there is enough information to solve this problem. We know the mean, standard deviation, and individual scores for both tests.
To compare Bill's performance on the first test with Dave's performance on the second test, we can use z-scores. A z-score measures how many standard deviations a particular score is from the mean.
To calculate the z-score for Bill's score on the first test (27), we use the formula:
z = (x - mean) / standard deviation
where x is the score, mean is the mean of the distribution, and standard deviation is the standard deviation of the distribution.
For Bill's score on the first test:
z = (27 - 25) / 4.6
By calculating this, we can find out how Bill's score compares to others who took the first test.
Similarly, to calculate the z-score for Dave's score on the second test (71), we use the same formula:
z = (x - mean) / standard deviation
where x is the score, mean is the mean of the distribution, and standard deviation is the standard deviation of the distribution.
For Dave's score on the second test:
z = (71 - 68) / 11.9
By calculating this, we can determine how Dave's score compares to others who took the second test.
However, from the given information, we cannot directly compare Bill's performance to Dave's performance because the tests use different scales to measure the same aptitude. To make a meaningful comparison, we need to calculate their scores' percentile ranks.
To calculate the percentile rank, we use the z-score and the standard normal distribution (a bell-shaped distribution with a mean of 0 and a standard deviation of 1). We can look up the percentile rank corresponding to each z-score in a standard normal distribution table, or use statistical software or online calculators.
By calculating the percentile ranks for Bill's score and Dave's score, we can determine their relative performance. However, we would need the percentile rank information to make a precise comparison.