SOLUTION: In a recent​ year, the scores for the reading portion of a test were normally​ distributed, with a mean of 21.8 and a standard deviation of 5.2. Use Table 4 in the back
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-> SOLUTION: In a recent​ year, the scores for the reading portion of a test were normally​ distributed, with a mean of 21.8 and a standard deviation of 5.2. Use Table 4 in the back
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Question 1124690: In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 21.8 and a standard deviation of 5.2. Use Table 4 in the back of your text to complete parts (a) through (d) below. Scroll to see the entire problem.
(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 16.
(b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 17.8 and 25.8.
(c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than 32.5.
(d) Are any of the events in parts a through c considered unusual? Why or why not?
You can put this solution on YOUR website! z=(x-mean)/sd
z<(16-21.8)/5.2 or <-1.12 for probability 0.1314
z is between (17.8-21.8)/5.2 and (25.8-21.8)/5.2 or between -0.77 and +0.77. That has probability 0.5587
z>(32.5-21.8)/5.2 or >2.06 for probability 0.0197
The last would be unusual with 2% probability, but in a group of 1000 students 20 would be expected to score this high or higher. Large groups with small probability will have some low probability occurrences. Smaller groups would be less likely. One also needs to define what is considered unusual, 5%? 1%?
