Question
In: Statistics and Probability
consider a normally distributed random variable with a population mean of 190 and a standard deviation...
consider a normally distributed random variable with a population mean of 190 and a standard deviation of 24. A sample mean of 36 observations will be taken the probability that the sample mean will be between 196 and 198 is?
Solutions
Expert Solution
Solution :
Given that,
mean = 
= 190
standard deviation = 
= 24
=
/ 
n = 24 /
36 = 4
= P[(196 - 190) /4 < (
-
)
/
< (198 - 190) / 4)]
= P(1.5 < Z < 2)
= P(Z < 2) - P(Z < 1.5)
= 0.9772 - 0.9332
= 0.044
Probability = 0.044
orchestra answered 3 years agoRelated Solutions
A random variable is normally distributed with a mean of 24 and a standard deviation of...
A random variable is normally distributed with a mean of 24 and
a standard deviation of 6. If an observation is randomly selected
from the distribution,
a. What value will be exceeded 5% of the time?
b. What value will be exceeded 90% of the time?
c. Determine two values of which the smaller has 20% of the
values below it and the larger has 20% of the values above it.
d. What value will 10% of the observations be...
A random variable is normally distributed. It has a mean of 245 and a standard deviation...
A random variable is normally distributed. It has a mean of 245
and a standard deviation of 21. a.) If you take a sample of size
10, can you say what the shape of the distribution for the sample
mean is? Why? b.) For a sample of size 10, state the mean of the
sample mean and the standard deviation of the sample mean. c.) For
a sample of size 10, find the probability that the sample mean is
more...
A random variable is normally distributed. It has a mean of 225 and a standard deviation...
A random variable is normally distributed. It has a mean of 225
and a standard deviation of 26.
If you take a sample of size 11, can you say what the shape of
the sampling distribution for the sample mean is? Why?
If the sample size is 11, then you can't say anything about the
sampling distribution of the sample mean, since the population of
the random variable is not normally distributed and the sample size
is less than 30....
The random variable x is normally distributed with a mean of 68 and a standard deviation...
The random variable x is normally distributed with a mean of 68
and a standard deviation of 4. Find the interquartile range (IQR)?
Use R.
A random variable is normally distributed. It has a mean of 245 and a standard deviation...
A random variable is normally distributed. It has a mean of 245
and a standard deviation of 21. I just need G.
a.)If you take a sample of size 10, can you say what the shape
of the distribution for the sample mean is? Why?
b.) For a sample of size 10, state the mean of the sample mean
and the standard deviation of the sample mean.
c.) For a sample of size 10, find the probability that the
sample...
A random variable is normally distributed. It has a mean of 245 and a standard deviation...
A random variable is normally distributed. It has a mean of 245
and a standard deviation of 21.
e.) For a sample of size 35, state the mean of the sample mean
and the standard deviation of the sample mean.
f.) For a sample of size 35, find the probability that the
sample mean is more than 241.
g.) Compare your answers in part c and f. Why is one smaller
than the other?
a. A population is normally distributed with a mean of 16.4 and a standard deviation of...
a. A population is normally distributed with a mean of 16.4 and
a standard deviation of 1.4. A sample of size 36 is taken from the
population.
What is the the standard deviation of the sampling
distribution?
Round to the nearest thousandth.
b. A population is normally distributed with a mean of 15.7 and
a standard deviation of 1.4. A sample of size 24 is taken from the
population.
What is the the standard deviation of the sampling
distribution?
Round...
Assume the random variable X is normally distributed with mean μ = 50 and standard deviation...
Assume the random variable X is normally distributed with mean μ
= 50 and standard deviation σ = 7. Compute the probability.
P(35<X<63)
2. A variable is normally distributed with a mean of 120 and a standard deviation of...
2. A variable is normally distributed with a mean of
120 and a standard deviation of 15. Twenty five scores are randomly
sampled.
a) What is the probability that the mean of the four
scores is above 111?
b) What is the probability that the mean of the four
scores will be between 114 and 123?
4.Suppose that a sample of 36 employees at a large company were
surveyed and asked how many hours a week they thought the company...
The variable x is normally distributed with a mean of 500 and a standard deviation of...
The variable x is normally distributed with a mean of 500 and a
standard deviation of 50. Find a) The 60th percentile. b)The 35th
percentile. c)The x value which exceeds 80% of all x values. d)The
x value that is exceeded by 80% of all x values.
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- TASK back to top In the contemporary management environment, mergers and acquisitions are hot topics; particularly...
- A room with 2.7-m-high ceilings has a metal plate on the floor with V = 0V...
- which of the following statements are true? a) the same nuclear changes (creation/destruction of specific nucleons)...
- Overview: Advances in technology have impacted many facets of the auditing process, from assessing risk and...
- Background: This course is all about data visualization. However, we must first have some understanding about...
- A rescue helicopter lifts a 70.6-kg person straight up by means of a cable. The person...
- Dolomite, [CaMg(CO3)2] is found in a soil sample. A geochemist titrates 24.65 g of soil with...
ADVERTISEMENT