A) What must be the probabnty l selecting a resman?a junior? B) What is the prob

Question

A) What must be the probabnty l selecting a resman?a junior? B) What is the probability of selecting a junior or a senior? C) What is the probability of selecting anyone who is not a senior? 4. The scores of students on the ACT in 2001 had a normal distribution with mean A) What is the probability that a single student randomly chosen from all those taki B) Find the score x such that only 20% students scored higher than x. C) Consider an SRS of 9 students who took the test. What is the probability that the = 23 and standard deviation 4.7. the test scores 21 or higher? (leave your answer in decimal) mean score of these students is 21 or higher?

Explanation / Answer

= 23

= 4.7

Let X is the score of any random student

(a) Pr(X > =21; 23; 4.7) = 1 - Pr(X < 21; 23; 4.7)

Z = (21 - 23)/ 4.7 = -0.43

so Pr(X > =21; 23; 4.7) = 1 - Pr(X < 21; 23; 4.7) = 1 - (-0.43) = 1 - 0.3336 = 0.6664

(b) Pr(Score > X ; 23 ; 4.7) = 0.2

Pr(Score < X ; 23 ; 4.7) = 1 - 0.2 = .8

Z - value form p- value = 0.8

Z = 0.84

(X - 23)/ 4.7 = 0.84

X = 23 + 4.7 * 0.84 = 26.95

(c) Standard error of the sample mean s = s/sqrt(n) = 4.7/ sqrt(9) = 1.567

Pr(x > =21; 23; 1.567) = 1 - Pr(X < 21; 23; 1.567)

Z = (21 - 23)/ 1.567 = -1.28

so Pr(X > =21; 23; 1.567) = 1 - Pr(X < 21; 23; 1.567) = 1 - (-1.28) = 1 - 0.1003 = 0.8997

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