00:01
For this question, we are told that scores for an exam are normally distributed and have a mean score of 525 and a standard deviation of 80.
00:21
For part a, we're asked what percentage of testers score less than 350 on the exam? so we're looking for the probability that x is less than 350.
00:38
And to convert to z scores, we're using z is equal to x minus mu over sigma.
00:43
So this is equal to the probability that z is less than 350 minus 525 over 80, which is equal to the probability that z is less than minus 2 .188 equals 0 .044.
01:16
So the probability of scoring less than 350 is 0 .0144.
01:23
Or in other words, 0 .0144 of the students who take this exam score less than 350.
01:37
For part b, we're asked what score is needed to make the top 12%.
01:43
So we're looking for a score k, such that scoring higher than it is equal to 12 % or a 0 .12.
01:55
The probability of scoring higher than k is equal to 0 .12.
02:03
Another way to state this is to say the probability of z being less than k minus 525 over 80 is equal to 0 .12.
02:19
So you can look in the standard normal table or use a calculator or software to find the zd value that has a cumulative area of 0 .12.
02:30
And that gives us a value, a z score of 1 .175.
02:40
So we can say that k minus 525 over 80 is equal to 1 .17, and therefore, k is equal to 619.
02:56
So you must score higher than 619 in order to be in the top 12 % of testers.
03:06
For part c, we're asked what the interquartile range is.
03:12
So the interquirtile range is the range from the first quartile to the third.
03:20
So the range is the difference of these quartiles.
03:27
Remember, the probability of scoring less than the first quartile is equal to 0 .25.
03:37
So we can say that the probability of z being less than q1 minus 525 over 80 is equal to 0 .25.
03:54
So we have q1 minus 525 over 80 is equal to 1 .175.
04:03
So this 1 .175 is the z score that has a cumulative area of 0 .25...