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)

ANSWER:

(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:

Solution:

R.V. X follows normal distribution with

= 9.1

= 2

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)

= **0.2266**

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

= **0.7066**

The length, ?, of a fish from a particular mountain lake in
Idaho is normally distributed with ?=9.8 inches and ?=1.1
inches.
(a) Is ? a discrete or continuous random variable? (Type:
DISCRETE or CONTINUOUS) ANSWER:
(b) Write the event ''a fish chosen has a length of less than
7.8 inches'' in terms of ?: .
(c) Find the probability of this event:
(d) Find the probability that the length of a chosen fish was
greater than 11.3 inches: ....

The weights of the fish in a certain lake are normally
distributed with a mean of 20 lb and a standard deviation of 9. If
9 fish are randomly selected, what is the probability that the mean
weight will be between 17.6 and 23.6 lb? Write your answer as a
decimal rounded to 4 places.

The weights of the fish in a certain lake are normally
distributed with a mean of 9.4 lb and a standard deviation of 2.3.
If 42 fish are randomly selected, what is the probability that the
mean weight will be more than 9.7 lb?

The weights of the fish in a certain lake are normally
distributed with a mean of 13 pounds and a standard deviation of 6.
If a sample of 9 fish are randomly selected, what is the
probability that the mean weight will be between 10.2 and 16.6
pounds?

The weights of the fish in a certain lake are normally
distributed with a mean of 9.9 lb and a standard deviation of 2.1.
If 75 fish are randomly selected, what is the probability that the
mean weight will be between 7.7 and 10.4 lb?

The weights of the fish in a certain lake are normally
distributed with a mean of 15.2 pounds and a standard deviation of
4 pounds. If 6 fish are randomly selected, find the probability
that the mean weight is between 13.6 and 17.6 pounds.
Round your answer 4 places after the decimal
point.

The weights of the fish in a certain lake are normally
distributed with a mean of 20 lb and a standard deviation of 9.
a. If one fish is randomly selected, what is the probability
that the mean weight will be between 17.6 and 23.6 lb?
b. If 9 fish are randomly selected, what is the probability that
the mean weight will be between 17.6 and 23.6 lb?

The weights of the fish in a certain lake are normally
distributed with a mean of 15.9 pounds and a standard deviation of
5.1 pounds. If 5 fish are randomly selected, find the probability
that the mean weight is between 11.4 and 18.6 pounds. Round your
answer 4 places after the decimal point.

The weights of the fish in a certain lake are normally
distributed with a mean of14lb and a standard deviation of 9. If
9
fish are randomly selected, what is the probability that the
mean weight will be between 11.6 and 17.6lb?
Round your answer to four decimal places.

Solve the problem. The weights of the fish in a certain lake are
normally distributed with a mean of 18 lb and a standard deviation
of 9. If 9 fish are randomly selected, what is the probability that
the mean weight will be between 15.6 and 21.6 lb?

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