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?________

13.According to a report by the U.S. Fish and Wildlife Service,
the mean length of six-year-old rainbow trout in the Arolik River
in Alaska is 481 millimeters with a standard deviation of 41
millimeters. Assume these lengths are normally distributed.
a. What proportion of six-year-old rainbow trout are less than
450 millimeters long?
b. What proportion of six-year-old rainbow trout are between 400
and 500 millimeter long?
c. Is it unusual for a six-year-old rainbow trout to be less
than...

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...

According to one study among a certain group, pregnancy lengths
are approximately normally distributed with a mean of 267 days and
a standard deviation of 7 days. Approximately 12.7% of babies are
premature, which means that they are born before 37 weeks in the
pregnancy. A random sample of 75 pregnant women from this group is
observed and the length of each pregnancy is recorded. Let X be the
number of premature babies born to these mothers. What is the...

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