Question

(5 pts) The length, *X*, of a fish from a particular
mountain lake in Idaho is normally distributed with *μ*=8.3
inches and *σ*=2 inches.

(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 5.3 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 11.3 inches: .

(e) Find the probability that the length of a chosen fish was between 5.3 and 11.3 inches: .

Answer #1

Solution :

Given that ,

mean = = 8.3

standard deviation = = 2

a) continuous

b) P(x < 5.3) = P((x - ) / < (5.3 - 8.3) / 2)

= P(z < -1.5)

= 0.0668

''a fish chosen has a length of less than 5.3 inches'' = 0.0668

d) P(x > 11.3) = 1 - P(x < 11.3)

= 1 - P((x - ) / < (11.3 - 8.3) / 2)

= 1 - P(z < 1.5)

= 1 - 0.9332

= 0.0668

Probability = 0.0668

e) P(5.3 < x < 11.3) = P((5.3 - 8.3)/ 2) < (x - ) / < (11.3 - 8.3) / 2) )

= P(-1.5 < z < 1.5)

= P(z < 1.5) - P(z < -1.5)

= 0.9332 - 0.0668

= 0.8664

Probability = 0.8664

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