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...

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?

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)...

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...

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

A scientist has read that the mean birth weight, ?, of babies
born at full term is 7.4 pounds. The scientist, believing that ? is
different from this value, plans to perform a statistical test. She
selects a random sample of birth weights of babies born at full
term and finds the mean of the sample to be 7.1 pounds and the
standard deviation to be 1.8 pounds.
Based on this information answer the following questions
What are the null...

1.The weight of potato chip bags marketed as 16-ounce bags
follows a distribution that has a mean of 17.0 ounces and a
standard deviation of 1.0 ounces. Suppose a sample of 100 of these
bags of potato chips has been randomly sampled.
The mean weight of the 100 bags would be considered a
____________________ and the mean weight of all bags would be
considered a __________________.
statistic; statistic
parameter; parameter
parameter; statistic
statistic; parameter
2. Suppose we repeatedly sampled from...

(2 pts) The distribution of actual weights of 8-oz chocolate
bars produced by a certain machine is normal with mean 7.8 ounces
and standard deviation 0.2 ounces.
(a) What is the probability that the average weight of a random
sample of 4 of these chocolate bars will be between 7.66 and 7.9
ounces?
ANSWER:
(b) For a random sample of of these chocolate bars, find the
value L such that P(x¯<L)= 0.0281.
ANSWER:

6.5-4) Suppose x has a distribution with μ =
39 and σ = 20.
(a)If random samples of size n = 16 are selected, can
we say anything about the x distribution of sample
means?
Yes, the x distribution is normal with mean
μx = 39 and
σx = 5.
No, the sample size is too small.
Yes, the x distribution is normal with mean
μx = 39 and
σx = 1.3.
Yes, the x distribution is normal with mean...

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