Question
In: Math
A random sample of 81 observations is drawn from a population with a mean of 104...
A random sample of 81 observations is drawn from a population with a mean of 104 and a variance of 156.25.
a) State the distribution of the sample mean, ?̅. (Show any conditions that you have checked.)
b) Calculate the probability that the sample mean is at most 102.5.
c) Calculate the probability that the sample mean is between 103.5 and 105.8.
Solutions
Expert Solution
Given that, mean 
= 104 and
variance 
=
156.25
=> standard deviation 
sample size (n) = 81
a) The distribution of the sample mean 
is
approximately normal because, sample size is greater than 30 and
also population standard deviation is known.
Mean and standard deviation of the sampling distribution of sample mean are,
b) We want to find, 
Therefore, required probability is 0.1401
c) We want to find, 
Therefore, required probability is 0.5438
milcah answered 1 year agoRelated Solutions
A random sample of n=64 observations is drawn from a population with a mean equal to...
A random sample of n=64 observations is drawn from a population
with a mean equal to 51 and a standard deviation equal to 32.
a. Find the probability that overbar x is less than 43.
b. Find the probability that overbar x is greater than 57.
c. Find the probability that x over bar x falls between 43 and
59.
(Round to three decimal places as
needed.)
A random sample of n = 100 observations is drawn from a population with mean 10...
A random sample of n = 100 observations is drawn from a
population with mean 10 and variance 400.
(a) Describe the shape of the sampling distribution of ¯x. Does
your answer depend on the sample size? (
b) Give the mean and standard deviation of the sampling
distribution of ¯x.
(c) Find the probability that ¯x is less than 8.
(d) Find the probability that ¯x is greater than 9.5.
(e) Find the probability that ¯x is between 8...
A random sample of 64 observations is to be been drawn from a distribution with mean...
A random sample of 64 observations is to be been drawn from a
distribution with mean
15 and standard deviation 10. Find the probability that the sample
mean, x̅ , will differ
from μ by no more than 2 units in either direction. Interpret your
results.
7.A random sample of 49 observations is drawn from a population with a normal distribution. If...
7.A random sample of 49 observations is drawn from a population
with a normal distribution. If the sample mean is 265 and the
sample standard deviation is 57, find the 95% confidence interval
for the population mean.
8. A random sample of 49 observations is drawn from a population
with a normal distribution with a standard deviation of 57. If the
sample mean is 265, find the 95% confidence interval for the
population mean. Compare this confidence interval with the...
A random sample of 10 observations was drawn from a large normally distributed population. The data...
A random sample of 10 observations was drawn from a large
normally distributed population. The data is below.
21, 22, 19, 25, 19, 19, 21, 26, 21, 23
Test to determine if we can infer at the 3% significance level
that the population mean is not equal to 22, filling in the
requested information below.
A. The value of the standardized test statistic:
Note: For the next part, your answer should use
interval notation. An answer of the form...
A random sample of 10 observations was drawn from a large normally distributed population. The data...
A random sample of 10 observations was drawn from a large
normally distributed population. The data is below.
20232221241926191923 Test to determine if we can infer at the 7%
significance level that the population mean is not equal to 22,
filling in the requested information below.
A. The value of the standardized test statistic: Note: For the
next part, your answer should use interval notation. An answer of
the form (−∞,a) is expressed (-infty, a), an answer of the form...
A random sample of 10 observations was drawn from a large normally distributed population. The data...
A random sample of 10 observations was drawn from a large
normally distributed population. The data is below.
2019242326232524262620192423262325242626
Test to determine if we can infer at the 7% significance level
that the population mean is not equal to 22, filling in the
requested information below.
A. The value of the standardized test statistic:
Note: For the next part, your answer should use
interval notation. An answer of the form (−∞,?)(−∞,a) is expressed
(-infty, a), an answer of the form...
The data below is a random sample of 3 observations drawn from the United States population....
The data below is a random sample of 3 observations drawn from
the United States population. Use the data to answer the following
questions
i. Find 95% confidence intervals of the population mean of
experience and wage.
ii. Estimate ρe,w, the correlation between the variables
experience and wage.
iii. Find βˆ 1 and βˆ 0, the estimates of the parameters in the
following regression equation wage = β0 + β1education + ϵ
iv. Predict wages for a person with 15...
A random sample of 10 observations was drawn from a large normally distributed population. The data...
A random sample of 10 observations was drawn from a large
normally distributed population. The data is below.
21 26 27 21 19 28 25 25 20 20
Test to determine if we can infer at the 7% significance level
that the population mean is not equal to 23, filling in the
requested information below.
The p-value is =
Your decision for the hypothesis test:
A. Reject ?0.
B. Reject ?1.
C. Do Not Reject ?1.
D. Do Not Reject...
A random sample is drawn from a population with mean μ = 66 and a standard...
A random sample is drawn from a population with mean μ = 66 and
a standard deviation σ =5.5.
Are the sampling distribution of the sample mean with n = 16 and
with n = 36 normally distributed?
A. Yes, both the sample means will have a normal
distribution.
B. No, for both sample sizes, the standard normal distribution
could not be used.
C. No, the standard normal distribution could be used only for
the sample size n = 16....
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Singh Development Co. is deciding whether to proceed with Project X. The cost would be $12...
- CS2123 Data Structures - Fall 2019 Assignment 1: Function Runtimes Table Due 9/11/19 by 11:59pm Completing...
- Question 2. Design a 16-1 MUX using any number of lower MUXs, such as 8-1 or...
- . Write a function that takes, as arguments, two objects, value1 and value2. If
- Wii Brothers, a game manufacturer, has a new idea for an adventure game. It can market...
- Consider the distillation of ethanol (C2H5OH) and the combustion of ethanol . Use a bullet point...
- 1.How does Economic exposure to exchange rate movements affect the capital budgeting of a firm? Provide...
ADVERTISEMENT