Question

Question 3 According to the act, results from testing found that students had a mean reading score of 21.4 with a standard deviation of 6.0. Assuming that the scores are normally distributed: a. Find the probability that a randomly selected student has a Reading ACT score less than 20. b. Find the probability that a randomly selected student has a Reading ACT between 18 and 24. C. Find the probability that a randomly selected student has a Reading ACT score greater than 30. d. Find the value of the 75th percentile for ACT scores.

Answer 1

(a) oc=20. . e=2104 r=6 Now, probability of randomly selected student having SAT score <20,P (6(<20) - z-value, z=x-M = 20-214 lo-2 7. z =-0.23 Distribution Plot Normal, Mean=0, StDev=1 Area 0.4090 -0.230 So, P (c<20) = P(22-0,23) = 0.409 Ansca)

18 to 24, For SAT score beth P ( 18 <x<24) I x=24 For x=18 Z=x+41 = 18-21.4 -2.4 Z=24-21.4 18-21.4 Za = 0.43 = -0.57 Distribution Plot Normal, Mean=0, StDev=1 0.3821 -0.57 0 0.43 Z - P(18<x<24) =P (-0.57 <2<0-43) = 0.3821 Anscb)

(©) score >30. P(x>30) forx=30 z=3-4-.30–21:4 = 1.43 Distribution Plot Normal, Mean=0, StDev=1 0.0764 1.43 ON PGC>30)=P(2>1.43) = 0.0764 Ansce

(d) for 75th percentile scores taking p=0.75 Distribution Plot Normal, Mean=0, StDev=1 0.75 0 0.6745 we got z=0.0745 - Now, Z=36-4 2 0.6745= 3(-21-4 ..x=25.45 Ans(d)

to find the area Z tables are used/

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