Question

A researcher is interested in the lengths of Salvelinus fontinalis (brook trout), which are known to be approximately Normally distributed with mean 80 centimeters and standard deviation 5 centimeters.

a. What proportion of these fish are larger than 86.5 centimeters in length?

b. If you take a random sample of 6 brook trout, what is the probability that their average length is greater than 86.5 cm?

c. What is the minimum length for the top 15% of brook trout?

Answer #1

Empirical Rule. It is known that the lengths of trout in a
particular river are approximately mound-shaped with mean 14” and
standard deviation 1”. About what proportion of the trout have
lengths between 11' and 14' and 14” and 16”?

Suppose a team of biologists has been studying a group of trout.
This team has determined that the lengths of the trout are normally
distributed with a mean of 10.7 inches and a standard deviation of
1.2 inches.
a) If one trout is selected at random, what is the probability
that its length will be between 7.5 and 8.2 inches?
b) If eight trout are selected at random, what is the
probability that their mean length will be less than...

Assume that the weights of Lahontan Cutthroat Trout are
normally distributed with a population mean weight of 5 pounds and
a standard deviation of 1.2 pounds.
(a) What is the probability of catching a fish that weighs less
than 4.5 pounds?
(b) What is the probability of catching a fish that weighs
greater than 5.25 pounds?
(c) What is the probability of catching a fish that weighs
between 4.5 and 5.25 pounds?

Step 1 of 4:
A glass tube maker claims that his tubes have lengths that are
normally distributed with a mean of 9.00 cm and a variance of 0.25
cm.
What is the probability that a quality control regulator will pull
a tube off the assembly line that has a length greater than 9 cm?
Round your answer to one decimal place.
Step 2 of 4:
A glass tube maker claims that his tubes have lengths that are
normally distributed...

The lengths of Atlantic croaker fish are normally distributed,
with a mean of 10.2 inches and a standard deviation of 1.9 inches
Suppose an Atlantic croaker fish is randomly selected.
a. You want to determine the proportion of the croaker
population that is longer than 15 inches. what z-score should you
use?
b. What proportion of the croaker population that is longer than
15 inches? Give ur answer to 4 decimal places, using z-score from
a
c. You select a...

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...

Trout were sampled from two different lake populations
and their lengths measured. The researchers are interested in
knowing whether the average length distribution for the trout in
lake 1 (group1) are greater than the average length distribution
for the trout in lake 2 (group 2). Using R and the Wilcoxon Rank
Sum-test answer the following questions for the data
available:
Lake1
Lake2
21.85
42.6
31.4
32.65
78.5
28.3
11.7
19.7
41.15
29.45
27.55
16.05
25.4
24.15
35.8
14.3
8.05
39.65...

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 millimeters long?
c. Is it unusual for a six-year-old rainbow trout to be less than...

A manufacturer produces widgets whose lengths are normally
distributed with a mean of 6.8 cm and standard deviation of 2.1
cm.
Round answer to four decimal places
A. If a widget is selected at random, what is the probability it
is greater than 6.8 cm.?_____
B. What is the standard deviation of the average of samples of
size 36 ?______
C. What is the probability the average of a sample of size 36 is
greater than 6.8 cm?_______

7. Suppose the lengths of pregnancies of a certain animal are
approximately normally distributed with mean 108 days and standard
deviation 9 days. a. What is the probability that a random sample
of size 4 will have a mean length of pregnancies of more than 112
days? b. What is the probability that a random sample of size 10
will have a mean length of pregnancies of more than 112 days? c. If
the length of pregnancies from part a...

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