In a sample, we have n=140 and
p=0.80. Using the normal distribution to find 99%
confidence interval for the population proportion p. Round
all answers to 3 decimal places.
What is the standard error?
What is the margin of error?
Construct a 99% confidence interval for the population
proportion p.
What is a t-distribution? Compare the t-distribution and the
standard normal distribution. When do you use the t-distribution?
The height of US women is normally distributed. A sample of 25
women shows an average hight of 160cm with a standard deviation of
5cm. Use t distribution to find the probability that the average
height of randomly selected 25 women is greater than 172cm.
The standard normal distribution is a continuous distribution
with a mean of 0 and a standard deviation of 1. The following is
true:
About 68% of all outcomes lie within 1 St.Dev.
About 95% of all outcomes lie within 2 St.Devs.
About 99.7% of all outcomes lie within 3 St. Devs.
The probability/percentage/percentile for a normal distribution is
the area under the curve. You will ALWAYS BE CALCULATING OVER AN
INTERVAL.
Values outside of 2 St.Devs. are considered “unusual values.”...
Demonstrate the use of the normal distribution, the standard
normal distribution, and the central limit theorem for calculating
areas under the normal curve and exploring these concepts in real
life applications. Scenario Frank has only had a brief introduction
to statistics when he was in high school 12 years ago, and that did
not cover inferential statistics. He is not confident in his
ability to answer some of the problems posed in the course. As
Frank's tutor, you need to...
Open the Excel program
Suppose we want to know the standard normal distribution up to
the given value.
That is P(Z < a). Lets use Excel instead of the standard
normal distribution table
In cell A1 type mean. In cell B1 type 0. That means that we are
letting mean be zero.
click on cell A2 and type SD. In cell B2 type 1. That means that
we are letting standard deviation be one. That is, the normal
distribution is...
Power questions. Suppose a population follows a normal
distribution with a standard deviation of 1. We take a random
sample of n= 100 individuals from this population. We know, then,
that sample mean for our population will have the property that
X∼N(μ,1/100).
(a)If μ= 10, find the probability that X >10.1645
(b)If μ= 10.3, find the probability that ̄X >10.1645
(c)Now, consider testing H0:μ= 10 vs H1:μ
>10, using α= 0.05. What is the rejection rule for this test?
Give...
What are the main differences between normal distribution and
standard normal distribution? What are the main characteristics of
standard normal distribution and why do we need standard normal
distribution?
The incomes of a population of lawyers have a normal
distribution with mean US$88,000 and standard deviation US$60,000.
Forty-nine lawyers are selected at random from the above population
to serve as a sample in a research project. Use the z for
a sample mean formula and determine the probability that the one
sample of 49 lawyers drawn at random will have a mean salary of
US$90,000 or greater.
a. .03
b. .23
c. -.03
d.-.23
e. .5120
f..4880
g. .5910...