The length, X, of a fish from a particular mountain lake in Idaho is normally di
ID: 2949133 • Letter: T
Question
The length, X, of a fish from a particular mountain lake in Idaho is normally distributed with ?=7.9 inches and ?=1.3 inches. Please round z-scores to 2 decimal places and give probabilities to at least 4 decimal places.
(a) Is X a discrete or continuous random variable? (Type: DISCRETE or CONTINUOUS)
ANSWER:
(b) Write the event ''a fish chosen has a length of less than 5.9 inches'' in terms of X :
(c) Find the probability of this event:
(d) Find the probability that the length of a chosen fish was greater than 9.9 inches:
(e) Find the probability that the length of a chosen fish was between 5.9 and 9.9 inches:
Explanation / Answer
a) Continuous
b) The event will be: X < 5.9
c) Probability of this event:
P(X < 5.9)
= P(z < (5.9 - 7.9)/1.3)
= P(z < -1.54)
= 0.0618
d) P(X > 9.9)
= P(z > (9.9 - 7.9)/1.3)
= P(z > 1.54)
= 0.0618
e) P(5.9 < X < 9.9)
= P(-1.54 < z < 1.54)
= 0.8764
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