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 23.2 and a standard deviation of 6.1. Complete parts (a) through (d) below. Find the probability that a randomly selected high school student who took the reading portion of the lest 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) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 19.5 and 26.9. the probability of a student scoring between 195 and 269 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 35.5. the probability of a student scoring more than 35.5 is (Round to four decimal places as needed.)

Explanation / Answer

= 23.2, = 6.1

(a) z = (x - )/ = (21 - 23.2)/6.1 = -0.3607

P(x < 21) = P(z < -0.3607) = 0.3592

(b) z1 = (19.5 - 23.2)/6.1 = -0.6066 and z2 = (26.9 - 23.2)/6.1 = 0.6066

P(19.5 < x < 26.9) = P(-0.6066 < z < 0.6066) = 0.4559

(c) z = (35.5 - 23.2)/6.1 = 2.0164

P(x > 35.5) = P(z > 2.0164) = 0.0219

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