Assume two normal distributions where mu_1 = 0.0001, sigma_1 = 0.01, mu_2 = -.0002, sigma_2 = 0.015, and ρ = .45. Using z_s = { .814, .259 }, generate z_1 and z_2.

Normal distributions
asked 2021-02-09
Assume two normal distributions where \(\displaystyle\mu_{{1}}={0.0001},\sigma_{{1}}={0.01},\mu_{{2}}=-{.0002},\sigma_{{2}}={0.015},{\quad\text{and}\quad}ρ={.45}\). Using \(\displaystyle{z}_{{s}}={\left\lbrace{.814},{.259}\right\rbrace}\), generate \(\displaystyle{z}_{{1}}{\quad\text{and}\quad}{z}_{{2}}\).

Answers (1)

Step 1
Given information-
Using \(\displaystyle{z}_{{s}}={\left\lbrace{0.814},{0.259}\right\rbrace}\)
So, X = 0.814, Y = 0.259
Step 2
So, the value of, \(\displaystyle{z}_{{1}}={81.39}{\quad\text{and}\quad}{z}_{{2}}=-{21.6628}\).

Relevant Questions

asked 2020-12-07
Suppose you take independent random samples from populations with means \(\displaystyle\mu{1}{\quad\text{and}\quad}\mu{2}\) and standard deviations \(\displaystyle\sigma{1}{\quad\text{and}\quad}\sigma{2}\). Furthermore, assume either that (i) both populations have normal distributions, or (ii) the sample sizes (n1 and n2) are large. If X1 and X2 are the random sample means, then how does the quantity
Give the name of the distribution and any parameters needed to describe it.
asked 2021-02-04
Let two independent random samples, each of size 10, from two normal distributions \(\displaystyle{N}{\left(\mu_{{1}},\sigma_{{2}}\right)}{\quad\text{and}\quad}{N}{\left(\mu_{{2}},\sigma_{{2}}\right)}\) yield \(\displaystyle{x}={4.8},{{s}_{{1}}^{{2}}}\)
= 7.88.
Find a 95% confidence interval for \(\displaystyle\mu_{{1}}−\mu_{{2}}\).
asked 2020-11-29
When we want to test a claim about two population means, most of the time we do not know the population standard deviations, and we assume they are not equal. When this is the case, which of the following is/are not true?
-The samples are dependent
-The two populations have to have uniform distributions
-Both samples are simple random samples
-Either the two sample sizes are large or both samples come from populations having normal distributions or both of these conditions satisfied.
asked 2021-03-11
Consider two independent populations that are normally distributions. A simple random sample of \(\displaystyle{n}_{{1}}={41}\) from the first population showed \(\displaystyle\overline{{x}}_{{11}}={33}\), and a simple random of size \(\displaystyle{n}_{{2}}={48}\) from the second population showed
Suppose \(\displaystyle{s}_{{1}}={9}{s}_{{1}}={9}{\quad\text{and}\quad}{s}_{{2}}={10}{s}_{{2}}={10}\), find a 98% confidence interval for \(\displaystyle\mu_{{1}}−\mu_{{2}}\mu_{{1}}-\mu_{{2}}\). (Round answers to two decimal places.)
margin of error-?
lower limit-?
upper limit-?
asked 2021-01-13
a) Which of the following properties distinguishes the standard normal distribution from other normal distributions?
-The mean is located at the center of the distribution.
-The total area under the curve is equal to 1.00.
-The curve is continuous.
-The mean is 0 and the standard deviation is 1.
b) Find the probability \(\displaystyle{P}{\left({z}{<}-{0.51}\right)}\) using the standard normal distribution.
c) Find the probability \(\displaystyle{P}{\left({z}{>}-{0.59}\right)}\) using the standard normal distribution.
asked 2021-01-27
Np>5 and nq>5, estimate P(at least 11) with n=13 and p = 0.6 by using the normal distributions as an approximation to the binomial distribution. if \(\displaystyle{n}{p}{<}{5}{\quad\text{or}\quad}{n}{q}{<}{5}\) then state the normal approximation is not suitable.
p (at least 11) = ?
asked 2021-01-19
Identify the null and alternative hypothesis in the following scenario.
To determine if battery 1 lasts longer than battery 2, the mean lasting times, of the two competing batteries are compared. Twenty batteries of each type are randomly sampled and tested. Both populations have normal distributions with unknown standard deviations.
Select the correct answer below: \(H_{0}:\mu_{1}\geq\mu_{2}, H_{a}:\mu_{1}<\mu_{2}\)
\(H_{0}:\mu_{1}\leq −\mu_{2}, H_{a}:\mu_{1}>−\mu_{2}\)
\(H_{0}:\mu_{1}\geq −\mu_{2}, H_{a}:\mu_{1}<−\mu_{2}\)
\(H_{0}:\mu_{1}=\mu_{2}, H_{a}:\mu_{1}\neq \mu_{2}\)
\(H_{0}:\mu_{1}\leq \mu_{2}, H_{a}:\mu_{1}>\mu_{2}\)
asked 2021-02-26
Consider two normal distributions, one with mean-4 and standard deviation 3, and the other with mean 6 and standard deviation 3. Answer true or false to each statement and explain your answers.
a. The two normal distributions have the same spread.
b. The two normal distributions are centered at the same place.
asked 2021-03-02
\(\displaystyle{\left(\mu{1}-\mu{2}\right)}\) For two normal distributions
Obtain the appropriate point estimator
asked 2020-11-22
Answer true or false to each statement.
a. Two normal distributions that have the same mean are centered at the same place, regardless of the relationship between their standard deviations.
b. Two normal distributions that have the same standard deviation have the same spread, regardless of the relationship between their means.