3. Assume that finishing times in a marathon are normally and a standard deviati

Question

3. Assume that finishing times in a marathon are normally and a standard deviation of 1.25 hours. Name: distributed with a mean of 5 houns a. (10 pt) Interprepu betemine the z-score of a runer wiho finishes the marahon in 33ouns what this value means regarding the runner's performance relative to the rest of the runners. b. (10 pt) Determine the proportion of runners who finish the marathon faster than 3 5 hours. (10 pt) Determine the time for which 90% of runners are slower. c. (20 pt) The probability that any randomly selected student passes Statistics is 0.S. Twelve students are randomly selected. Determine the probability that more than 10 of the 12 selected students pass Statistics.

Explanation / Answer

3)a) Z-score = (x - mean)/SD

= (3.3 - 5)/1.25 = -1.36

B) P(X > 3.5) = P((x - mean)/SD > (3.5 - mean)/SD)

= P(Z > (3.5 - 5)/1.25)

= P(Z > -1.2)

= 1 - P(Z < -1.2)

= 1 - 0.1151 = 0.8849

C) P(X < x) = 0.9

Or, P( (x - mean)/SD < (x - 5)/1.25) = 0.9

Or, P(Z < (x - 5)/1.25) = 0.9

Or, (x - 5)/1.25 = 1.28

Or, x = 1.28 * 1.25 + 5

Or, x = 6.6

4) P = 0.8

n = 12

P(X = x) = nCx * Px * (1 - P)n - x

P(X > 10) = P(X = 11) + P(X = 12)

= 12C11 * (0.8)^11 * (0.2)^1 + 12C12 * (0.8)^12 * (0.2)^0 = 0.275

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