SOLUTION: In a recent​ year, the scores for the reading portion of a test were normally​ distributed, with a mean of 23.7 and a standard deviation of 5.9. Complete parts​ (

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Question 1043994: In a recent​ year, the scores for the reading portion of a test were normally​ distributed, with a mean of 23.7 and a standard deviation of 5.9. Complete parts​ (a) through​ (d) below.
​(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 18.
The probability of a student scoring less than 18 is?​(Round to four decimal places as​ needed.)
​(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 18.8 and 28.6.The probability of a student scoring between 18.8 and 28.6 is? Round to four decimal places as​ needed
​(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 35.8.
The probability of a student scoring more than 35.8 is?Round to four decimal places as​ needed
​(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
A.The event in part (a) is unusual because its probability is less than 0.05.
B.The events in parts (a) and (b) are unusual because its probabilities are less than 0.05.
C.None of the events are unusual because all the probabilities are greater than 0.05.
D.The event in part (c) is unusual because its probability is less than 0.05.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Z=(X-MEAN)/SD
a. (18-23.7)/5.9=-0.966
probability z <-0.966=0.1670
b. Here the z is between (18.8-23.7)/5.9, or -0.8305 and (28.6-23.7)/5.9=+0.8305. That probability is 0.5937
c.z=(35.8-23.7)/5.9=2.050. Probability z>2.050 is 0.0202.
d.The event in part c is unusual because the probability is low, 0.0202. Probabilities of 0.05 are not per se true borders but artificial ones, created by Sir Ronald Fisher when asked what probability should be used to consider something abnormal. He felt 1 in 20, or 5%. The most unusual number here is 0.0202, and that is a low likelihood, about 1 in 50, of a score being this great or greater.