Question

Park Rangers in a Yellowstone National Park have determined that fawns less than 6 months old have a body weight that is approximately normally distributed with a mean µ = 26.1 kg and standard deviation σ = 4.2 kg. Let x be the weight of a fawn in kilograms. Complete each of the following steps for the word problems below: Rewrite each of the following word problems into a probability expression, such as P(x>30). Convert each of the probability expressions involving x into probability expressions involving z, using the information from the scenario. Sketch a normal curve for each z probability expression with the appropriate probability area shaded. Solve the problem. 1. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs less than 25 kilograms? 2. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs more than 19 kilograms? 3. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs between 30 and 38 kilograms? 4. If a fawn less than 6 months old weighs 16 pounds, would you say that it is an unusually small animal? Explain and verify your answer mathematically. 5. What is the weight of a fawn less than 6 months old that corresponds with a 20% probability of being randomly selected? Explain and verify your answer mathematically.

Answer #1

Suppose a certain species of fawns between 1 and 5 months old
have a body weight that is approximately normally distributed with
mean kilograms and standard deviation kilograms. Let
x be the weight of a fawn in kilograms. Convert the
following x interval to a z interval. Round to
the nearest hundredth.

Fawns between 1 and 5 months old have a body weight that is
approximately normally distributed with mean μ = 28.8
kilograms and standard deviation σ = 4.6 kilograms. Let
x be the weight of a fawn in kilograms.
Convert the following x intervals to z
intervals. (Round your answers to two decimal places.)
(a) x < 30
z < ______
(b) 19 < x
____ < z
Convert the following z intervals to x intervals.
(Round your answers to one decimal...

Fawns between 1 and 5 months old have a body weight that is
approximately normally distributed with mean μ = 29.8
kilograms and standard deviation σ = 4.8 kilograms. Let
x be the weight of a fawn in kilograms.
Convert the following x intervals to z
intervals. (Round your answers to two decimal places.)
(a) x < 30
z <
(b) 19 < x
< z
(c) 32 < x < 35
< z <
Convert the following z intervals to x intervals....

Fawns between 1 and 5 months old have a body weight that is
approximately normally distributed with mean μ = 28.1
kilograms and standard deviation σ = 3.2 kilograms. Let
x be the weight of a fawn in kilograms.
For parts (a), (b), and (c), convert the x intervals to
z intervals. (For each answer, enter a number. Round your
answers to two decimal places.)
(a)
x < 30
z <
(b)
19 < x (Fill in the blank. A...

Fawns between 1 and 5 months old have a body weight that is
approximately normally distributed with mean μ = 27.2 kilograms and
standard deviation σ = 4.2 kilograms. Let x be the weight of a fawn
in kilograms. Convert the following x intervals to z intervals.
(Round your answers to two decimal places.)
(a) x < 30 z < .67 Correct: Your answer is correct.
(b) 19 < x .67 Incorrect: Your answer is incorrect. <
z
(c) 32...

Fawns between 1 and 5 months old have a body weight that is
approximately normally distributed with mean μ = 29.8 kilograms and
standard deviation σ = 3.8 kilograms. Let x be the weight of a fawn
in kilograms. For parts (a), (b), and (c), convert the x intervals
to z intervals. (For each answer, enter a number. Round your
answers to two decimal places.) (a) x < 30 z < (b) 19 < x
(Fill in the blank. A...

Fawns between 1 and 5 months old have a body weight that is
approximately normally distributed with mean μ = 27.9 kilograms and
standard deviation σ = 3.2 kilograms. Let x be the weight of a fawn
in kilograms. The Standard Normal Distribution (mu = 0, sigma = 1).
A normal curve is graphed above a horizontal axis labeled z. There
are 7 equally spaced labels on the axis; from left to right they
are: -3, -2, -1, 0, 1,...

Fawns between 1 and 5 months old have a body weight that is
approximately normally distributed with mean μ = 28.3 kilograms and
standard deviation σ = 3.1 kilograms. Let x be the weight of a fawn
in kilograms. The Standard Normal Distribution (mu = 0, sigma = 1).
A normal curve is graphed above a horizontal axis labeled z. There
are 7 equally spaced labels on the axis; from left to right they
are: -3, -2, -1, 0, 1,...

A Companys customers owe $28,370 in accounts that are less than
6 months old and 45,430 in accounts that are over 6 months old. The
company expects to collect 97.8% of the newer accounts and 74.3% of
the others. How much is the estimated loss?
Departments A, B, and C of a factory occupied space as follows:
Department A- 120x110 feet; Department B- 60x180; and C- 80x90. If
the Total rent was $6,864, how much should be charged to each...

Question 5:
Baby weights: The weight of male babies less
than
2
months old in the United States is normally distributed with
mean
11.6
pounds and standard deviation
2.8
pounds. Use the TI-84 Plus calculator to answer the
following.
(a) What proportion of babies weigh more than
13
pounds?
(b) What proportion of babies weigh less than
15
pounds?
(c) What proportion of babies weigh between
9
and
13.2
pounds?
(d) Is it unusual for a baby to weigh more...

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