Homework6: Problem Previous Problem ListNext (1 point) The length, X, of a fish

Question

Homework6: Problem Previous Problem ListNext (1 point) The length, X, of a fish from a particular mountain lake in Idaho is normally distributed with 7.2 inches and 2 inches. (a) Is X a discrete or continuous random variable? (Type: DISCRETE or CONTINUOUS) ANSWER: CONTINUOUS (b) Find the probability that the length of a chosen fish was greater than 9.7 inches: (c) Find the probability that the length of a chosen fish was between 5.2 and 9.7 inches: Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 1 time. Your overall recorded score is 33%. You have 3 attempts remaining.

Explanation / Answer

Mean length of a fish in a particular lake in Idaho = 7.2 inches

standard deviation of length of a fish in lake   = 2 inches

(i) The distriubtion is contionous.

(ii) Pr ( X > 9.7 inches) WHere X is the length of the fish

Pr ( X > 9.7 inches) = NORM( X > 9.7 inches ; 7.2; 2) = 1 - Pr(X < 9.7 inches ; 7.2; 2)

Z = (9.7 - 7.2)/2 = 1.25

so Pr ( X > 9.7 inches) = NORM( X > 9.7 inches ; 7.2; 2) = 1 - Pr(X < 9.7 inches ; 7.2; 2) = 1 - (1.25)

= 1 - 0.8944

= 0.1056

(c) Pr ( 5.2 inch < X < 9.7 inch) = Pr ( X < 9.7 inch; 7.2 inch; 2 inch) - Pr (X < 5.2 inch, 7.2 inch; 2 inch)

Z - value

Z2 = (9.7 - 7.2)/ 2 = 1.25

Z1 = (5.2 - 7.2)/2 = -1

so Pr ( 5.2 inch < X < 9.7 inch) = (1.25) - (-1)

= 0.8944 - 0.1587 = 0.7357

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