In: Statistics and Probability
The length, XX, of a fish from a particular mountain lake in Idaho is normally distributed with μ=9.1μ=9.1 inches and σ=2σ=2 inches.
(a) Is XX a discrete or continuous random variable? (Type:
DISCRETE or CONTINUOUS)
(b) Write the event ''a fish chosen has a length equal to 6.1 inches'' in terms of XX: .
(c) Find the probability of this event:
d) Find the probability that the length of a chosen fish was greater than 10.6 inches: .
(e) Find the probability that the length of a chosen fish was between 6.1 and 10.6 inches:
R.V. X follows normal distribution with
a) Normal is a continuous type distribution.
So , answer is CONTINUOUS
b) event ''a fish chosen has a length equal to 6.1 inches''
In terms of X , event can be written as " X = 6.1"
c) P(X = 6.1) = 0
Because , for a continuous random variable , the probability at a particular point is considered as zero.
d)P( greater than 10.6 inches)
P(X > 10.6) = P[(X - )/ > (10.6 - )/]
= P[Z > (10.6 - 9.1)/2]
= P[Z > 0.75]
= 1 - P[Z < 0.75]
= 1 - 0.7734 ( use z table)
e)P(between 6.1 and 10.6 inches)
= P(6.1 < x< 10.6)
= P(X < 10.6) - P(X < 6.1)
= P[(X - )/ < (10.6 - 9.1)/2] - P[(X - )/ < (6.1 - 9.1)/2]
= P[Z < 0.75] - P[Z < -1.50]
= 0.7734 - 0.0668 ..Use z table