Question

According to a study, the random variable, at least X,
expressing the length of the fish endemic to a lake follows a
normal distribution with mean µ = 20cm and standard deviation σ =
4cm. a) A fish is fishing by the lake. What is the probability that
its length is greater than 18cm but does not exceed 24cm? b)
Determine a symmetric mean of the X interval whose lengths are 95%
of the lake's fish. c) Angling 4 fish from the lake: i) What is the
probability that their **average** length is less than
15cm? ii) What is the probability that at least 3 of them are
between 18cm and 24cm in length?

Answer #1

The length, X X , of a fish from a particular mountain lake in
Idaho is normally distributed with μ=9.6 μ = 9.6 inches and σ=1.4 σ
= 1.4 inches. (a) Is X X a discrete or continuous random
variable?
(b) Write the event ''a fish chosen has a length of less than
6.6 inches'' in terms of X X :
(c) Find the probability of this event:
(d) Find the probability that the length of a chosen fish was...

The length, X, of a fish from a particular mountain lake in
Idaho is normally distributed with μ= 8.9 and σ=1.6 inches.
(a) Write the event ''a fish chosen has a length of less than
5.9 inches'' in terms of X: ____
(b) Find the probability of this event: ____
(c) Find the probability that the length of a chosen fish was
greater than 11.4 inches: ____
(d) Find the probability that the length of a chosen fish was
between...

15 #8
The length, X, of a fish from a particular mountain lake in
Idaho is normally distributed with μ=8.7 inches and
σ=1.1inches.
(a) Find the probability that the length of a chosen fish was
greater than 9.7 inches: .
(b) Find the probability that the length of a chosen fish was
between 7.7 and 9.7 inches:

15 #5
The length, X, of a fish from a particular mountain lake in
Idaho is normally distributed with μ=9.8 inches and
σ=1.1inches.
(c) Find the probability of this event:
(d) Find the probability that the length of a chosen fish was
greater than 12.8 inches: .
(e) Find the probability that the length of a chosen fish was
between 8.8 and 12.8 inches:

(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...

The length, X, of a fish from a particular mountain lake in
Idaho is normally distributed with μ=7 inches and σ=1.7 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 equal to 4
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 8.5 inches: .
(e) Find the...

If X is a normal random variable that has a mean of µ = 20 and a
standard deviation σ = 2, (a) the standardized value of X=16 is
_________. (b) What is the probability that X is less than or equal
to 16? __________ (c) What is the probability that X is greater
than 16? __________ (d) What is the probability that X is equal to
16?________

The size of fish is very important to commercial fishing.
Suppose the length of Atlantic cod caught in nets has a mean of
49.5 cm and a standard deviation of 3.71 cm. The length of fish is
normally distributed. A sample of 14 fish is taken.
State the random variable.
The mean length of Atlantic cod caught in nets.
The standard deviation of lengths of Atlantic cod caught in
nets.
The length of Atlantic cod caught in nets.
Find the...

Let the random variable X follow a normal distribution with μ =
60 and σ^2=64.
a.
Find the probability that X is greater than 70.
b.
Find the probability that X is greater than 45 and less than
74.
c.
Find the probability that X is less than 65.
d.
The probability is 0.2 that X is greater than what
number?
e.
The probability is 0.05 that X is in the symmetric interval
about the mean between which two numbers?

Assume that individual daily wages of taxi drivers are described
as a random variable (X) that is normally distributed with
parameters (µ = 85, σ = 20). A sample of n = 4 drivers was selected
at random and Y = X¯ represents the sample mean, Y = X¯ = 1/4 · [X1
+ X2 + X3 + X4]
1. Find the chance that sample average (Y ) would be at least 70
and not exceeding 90
2. Evaluate probability...

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