In a recent year, the scores for the reading portion of a test were normally dis

Question

In a recent year, the scores for the reading portion of a test were normally distributed with a mean of 20.5 and a standard deviation of 5.7 Complete parts (a) through (d) below. 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.) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 13.2 and 27.8. The probability of a student scoring between 13.2 and 27.8 is (Round to four decimal places as needed.) 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 32.2. The probability of a student scoring more than 32.2 is (Round to four decimal places as needed.) Identify any unusual events. Explain your reasoning. Choose the correct answer below. The events in parts (a) and (b) are unusual because its probabilities are less than 0.05. The event in part (c) is unusual because its probability is less than 0.05. The event in part (a) is unusual because its probability is less than 0.05. None of the events are unusual because all the probabilities are greater than 0.05.

Explanation / Answer

= 20.5, = 5.7

(a) z = (x - )/ = (18 - 20.5)/5.7 = -0.4386

P(x < 18) = P(z < -0.4386) = 0.3305

(b) z1 = (13.3 - 20.5)/5.7 = -1.2807 and z2 = (27.8 - 20.5)/5.7 = 1.2807

P(13.2 < x < 27.8) = P(-1.2807 < z < 1.2807) = 0.7997

(c) z = (32.2 - 20.5)/5.7 = 2.0526

P(x > 32.2) = P(z > 2.0526) = 0.0201

(d) Option C.

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