3. A company ships computer components in boxes that contain 100 items. Assume t

Question

3. A company ships computer components in boxes that contain 100 items. Assume that the probability of a defective computer component is 0.2. Find the probability (using geometric distribution) that the first defect is found in the seventh component tested. Round your answer to four decimal places. (3 pts) 4. Find the z-scores that corresponds to each value. The test scores for placement tests are normally distributed. The mean test score was 24.3 and the standard deviation was 6.1. The test scores of 2 students selected at random are: (4 pts) a) 20 b) 26 a) b) 5. In a recent year, the ACT scores for the math portion of the test were normally distributed, with a mean of 21.1 and a standard deviation of 5.3. Find the probability that a randomly selected high school student who took the math portion of the ACT has a z that is between 19 and 24. (4 pts)

Explanation / Answer

Solution:-
3) Given n = 100, p= 0.2

P(X = 7) = 100C7 * 0.27 * 0.893 = 0.0002

4) Given that mean = 24.3 , sd = 6.1

a) 20 => Z = (20 - 24.3)/6.1 = -0.7049

b) 26 =>  Z = (26 - 24.3)/6.1 = 0.2787

5) mean = 21.1 sd = 5.3

=> P(19 < X < 24) = P((19 - 21.1)/5.3 < Z < (24 - 21.1)/5.3 )

= P(-0.3962< Z < 0.5471)

= 0.3642

Formula :- Z = (X - mu)/sd

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