Question

# (5 pts) The length, X, of a fish from a particular mountain lake in Idaho is...

(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)

(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: .

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