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

ID: 3326266 • Letter: I

Question

In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 22 8 and a standard deviation of 6.8 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 21 The probability of a student scoring less than 21 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 12 9 and 32.7 The probability of a student scoring between 12 9 and 327 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 36.9 The probablity of a student scoring more than 36 9 is Round to four decimal places as needed ) (d) Idenility any unusual events Explain your reasoning Choose the correct answer below o A. The events in parts (a) and (b) are unusual because its probabilities are less than 0 05 O B. The event in part (c) is unusual because hs probability is less than 0 05 O C. None of the events are unusual because all the probabilities are greater than 0.05 O D. The event in part (a) is unusual because hs probability is less than 0 05 Clhck to select your answers) Type here to search

Explanation / Answer

solution=

given mean = 22.8 and std = 6.8

Z=(X-MEAN)/SD
a).p(x<21) is

(21-22.8)/ 6.8=-0.265

.p(z <21) = 0.3955

b) p(12.9 < x< 32.7)

Here the z is between (12.9- 22.8)/ 6.8, or -1.4559 and (32.7-22.8)/ 6.8=+1.4559

. That probability is 0.8546
c.)p(x>36.9)

z=(36.9-22.8)/6.8=2.074. Probability z>2.074 is 0.0190

d)The event in part c is unusual because the probability is low, 0.0190. 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 0.0190, and that is a low likelihood, about 1 in 50, of a score being this great or greater

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

In a recent year, the scores for the reading proton of a test were normally dist

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

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