Question

3. [16 pts] Suppose that the birth weight of puppies follows a certain left-skewed distribution with mean 1.1 pounds and standard deviation 0.14 pounds (these numbers are made-up). We are interested in looking at the mean weights of samples of size n puppies. We would like to model these mean weights using a Normal Distribution.

a. [3 pts] What statistical concept allows us to do so and what is the sample size

requirement?

Now suppose that we take sample of size n = 35 puppies and
calculate the mean.

b. [4 pts] How are these means distributed? (Express the
distribution using statistical notation.)

c. [4 pts] What is the probability that the mean birth weight of 35
randomly chosen puppies is between 0.5 pounds and 1.77 pounds? Show
your work.

d. [5 pts] 1.2 ∗ 10−5% of the puppies are expected to weight more than x pounds at birth. What is x? Show your work.

Answer #1

It is known that the birth weight of newborn babies in
the U.S. has a mean of 7.1 pounds with a standard deviation of 1.5
pounds. Suppose we randomly sample 36 birth certificates from the
State Health Department, and record the birth weights of these
babies.
The sampling distribution of the average birth weights
of random samples of 36 babies has a mean equal to ______ pounds
and a standard deviation of ______ pounds.
What is the probability the...

It is known that the birth weight of newborn babies in the U.S.
has a mean of 7.1 pounds with a standard deviation of 1.5 pounds.
Suppose we randomly sample 36 birth certificates from the State
Health Department, and record the birth weights of these
babies.
The sampling distribution of the average birth weights of
random samples of 36 babies has a mean equal to ______
pounds and a standard deviation of ______ pounds.
What is the probability the average...

Suppose that the actual weight of 64-ouncebags of sugarhave a
skewed distribution witha mean of 65.0ounces anda standard
deviation of 0.5. Weights will be measured for a random sampleof
32bags and the sample mean will be computed.(1)What
distributionwill be sample mean have in this setting?(a)Exact
normaldistribution (b)Approximate t
distribution(c)Approximatenormal distribution(d)Standard
normaldistribution(2)What is the probabilitythat the sample mean
weight of the 32 bags of sugar is between 64.9 ounces and 65.2
ounces?

Statistics Canada reports that the birth weight of newborn
babies in Saskatchewan has a mean of 3.45 kg for both sexes.
Suppose the standard deviation is 0.7 kg. Further we randomly
sample 49 birth certifi- cates in Saskatchewan and record the birth
weights of samples babies. Find the mean and standard deviation of
the sampling distribution of x ̄. What is the probability that
sample mean birth weight will be less than 3.25 kg?

4. Suppose the birth weights of babies in the USA are normally
distributed, with mean 7.47 lb and standard deviation 1.21 lb. a.
Find the probability that a randomly chosen baby weighed between
6.4 and 8.1 pounds. (Show work.) b. Suppose a hospital wants to try
a new intervention for the smallest 4% of babies (those with the
lowest birth weights). What birth weight in pounds is the largest
that would qualify for this group? (Show your work.)

Suppose that the birth weights of infants are Normally
distributed with mean 120 ounces
and a standard deviation of 18 ounces. (Note: 1 pound = 16
ounces.)
a) Find the probability that a randomly selected infant will
weight less than 5 pounds.
b) What percent of babies weigh between 8 and 10 pounds at
birth?
c) How much would a baby have to weigh at birth in order for
him to weight in the top
10% of all infants?
d)...

Lifetimes of a certain brand of lightbulbs is known to follow a
right-skewed distribution with mean 24 months and standard
deviation 2 months. Let X̄ represent the sampling distribution of
the sample mean corresponding to a sample of size 1500 from this
distribution. We expect this sampling distribution to be...
Select one:
a. Approximately Normal with a mean of 24 months and a standard
deviation of 0.0013 months.
b. Right-skewed with a mean of approx. 24 months and a standard...

The weight of all 20-year-old men is a variable that has a
distribution that is skewed to the right,and the mean weight of
this population, μ, is 70 kilograms. The population standard
deviation, σ,is 10 kilograms (http://www.kidsgrowth.com). Suppose
we take a random sample of 75 20-year-old men and record the weight
of each.
What value should we expect for the mean weight of this sample?
Why?
Of course, the actual sample mean will not be exactly equal to
the value...

A recent report from the National Center for Health Statistics
(NCHS) states that the distribution of weights for men in the
United States aged 35 to 45 is well approximated by a normal
distribution with mean 176.4 pounds and standard deviation 31.3
pounds. Let X be the sample mean weight of a simple random sample
of 16 men chosen from this population.
(a) Find the interval containing the central 80% of the X
distribution. Interpret your answer in words.
(b)...

Suppose the weight of males follows a symmetrical, bell-shaped
distribution with mean 165 pounds and standard deviation 30.
Between what two weights will the data capture the middle
99.7%?
Need more information, like how many there are
165 - (2 x 30) to 165 + (2 x 30)
165 - (3 x 30) to 165 + (3 x 30)
None of the above
165 -30 to 165 + 30

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