Question

Let *x* be a random variable that represents the weights
in kilograms (kg) of healthy adult female deer (does) in December
in a national park. Then *x* has a distribution that is
approximately normal with mean *μ* = 69.0 kg and standard
deviation *σ* = 9.0 kg. Suppose a doe that weighs less than
60 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed
and released) at random in December is undernourished? (Round your
answer to four decimal places.)

(b) If the park has about 2800 does, what number do you expect to
be undernourished in December? (Round your answer to the nearest
whole number.)

does

(c) To estimate the health of the December doe population, park
rangers use the rule that the average weight of *n* = 60
does should be more than 66 kg. If the average weight is less than
66 kg, it is thought that the entire population of does might be
undernourished. What is the probability that the average weight

*x*

for a random sample of 60 does is less than 66 kg (assuming a
healthy population)? (Round your answer to four decimal
places.)

(d) Compute the probability that

*x*

< 71 kg for 60 does (assume a healthy population). (Round
your answer to four decimal places.)

Suppose park rangers captured, weighed, and released 60 does in
December, and the average weight was

*x*

= 71 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is below the mean, it is quite likely that the doe population is undernourished.Since the sample average is above the mean, it is quite likely that the doe population is undernourished. Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.

Answer #1

a)

mean = 69 , s = 9

P(x < 60)

z= (x -mean)/s

= ( 60 - 69)/9

= -1

P(x < 60) = P(z < -1) = 0.1587

b)

np = 2800 * 0.1587 = 444.36 = 444

c)

n = 60

P(x< 66)

z= (x -mean)/(s/sqrt(60))

= ( 66 - 69)/(9/sqrt(60))

= -2.582

P(x < 66) = P(z < -2.582) = 0.0049

d)

n = 60

P(x< 71)

z= (x -mean)/(s/sqrt(60))

= ( 71 - 69)/(9/sqrt(60))

=1.721

P(x < 71) = P(z < 1.721) = 0.9574

Since the sample average is above the mean, it is quite likely that the doe population is undernourished

Let x be a random variable that represents the weights
in kilograms (kg) of healthy adult female deer (does) in December
in a national park. Then x has a distribution that is
approximately normal with mean μ = 67.0 kg and standard
deviation σ = 8.0 kg. Suppose a doe that weighs less than
58 kg is considered undernourished.
(a) What is the probability that a single doe captured (weighed
and released) at random in December is undernourished? (Round your...

Let x be a random variable that represents the weights in
kilograms (kg) of healthy adult female deer (does) in December in a
national park. Then x has a distribution that is approximately
normal with mean μ = 64.0 kg and standard deviation σ = 8.9 kg.
Suppose a doe that weighs less than 55 kg is considered
undernourished. (a) What is the probability that a single doe
captured (weighed and released) at random in December is
undernourished? (Round your...

Let x be a random variable that represents the weights in
kilograms (kg) of healthy adult female deer (does) in December in a
national park. Then x has a distribution that is approximately
normal with mean μ = 70.0 kg and standard deviation σ = 8.1 kg.
Suppose a doe that weighs less than 61 kg is considered
undernourished.
(a) What is the probability that a single doe captured (weighed
and released) at random in December is undernourished? (Round your...

Let x be a random variable that represents the weights
in kilograms (kg) of healthy adult female deer (does) in December
in a national park. Then x has a distribution that is
approximately normal with mean ? = 64.0 kg and standard
deviation ? = 8.3 kg. Suppose a doe that weighs less than
55 kg is considered undernourished.
(a) What is the probability that a single doe captured (weighed
and released) at random in December is undernourished? (Round your...

Let x be a random variable that represents the weights
in kilograms (kg) of healthy adult female deer (does) in December
in a national park. Then x has a distribution that is
approximately normal with mean μ = 67.0 kg and standard
deviation σ = 8.1 kg. Suppose a doe that weighs less than
58 kg is considered undernourished.
(a) What is the probability that a single doe captured (weighed
and released) at random in December is undernourished? (Round your...

Let x be a random variable that represents the weights in
kilograms (kg) of healthy adult female deer (does) in December in a
national park. Then x has a distribution that is approximately
normal with mean μ = 59.0 kg and standard deviation σ = 8.1 kg.
Suppose a doe that weighs less than 50 kg is considered
undernourished.
(a) What is the probability that a single doe captured (weighed
and released) at random in December is undernourished? (Round your...

Let x be a random variable that represents the weights in
kilograms (kg) of healthy adult female deer (does) in December in a
national park. Then x has a distribution that is approximately
normal with mean μ = 61.0 kg and standard deviation σ = 8.8 kg.
Suppose a doe that weighs less than 52 kg is considered
undernourished. (a) What is the probability that a single doe
captured (weighed and released) at random in December is
undernourished? (Round your...

Let x be a random variable that represents the weights in
kilograms (kg) of healthy adult female deer (does) in December in a
national park. Then x has a distribution that is approximately
normal with mean μ = 51.0 kg and standard deviation σ = 8.5 kg.
Suppose a doe that weighs less than 42 kg is considered
undernourished. (a) What is the probability that a single doe
captured (weighed and released) at random in December is
undernourished? (Round your...

Let x be a random variable that represents the weights in
kilograms (kg) of healthy adult female deer (does) in December in a
national park. Then x has a distribution that is approximately
normal with mean μ = 58.0 kg and standard deviation σ = 7.4 kg.
Suppose a doe that weighs less than 49 kg is considered
undernourished. (a) What is the probability that a single doe
captured (weighed and released) at random in December is
undernourished? (Round your...

Let x be a random variable that represents the weights in
kilograms (kg) of healthy adult female deer (does) in December in a
national park. Then x has a distribution that is approximately
normal with mean μ = 67.0 kg and standard deviation σ = 8.7 kg.
Suppose a doe that weighs less than 58 kg is considered
undernourished.
(a) What is the probability that a single doe captured (weighed
and released) at random in December is undernourished? (Round your...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 18 minutes ago

asked 19 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago