1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
PolarNik [594]
3 years ago
12

When a production process is operating correctly, thenumber of units produced per hour has a normal distri- bution with a mean o

f 92.0 and a standard deviation of3.6. A random sample of 4 different hours was taken.a. Find the mean of the sampling distribution of thesample means. b. Find the variance of the sampling distribution ofthe sample mean.c. Find the standard error of the sampling distribu-tion of the sample mean.d. What is the probability that the sample mean ex-ceeds 93.0 units?
Mathematics
1 answer:
KengaRu [80]3 years ago
3 0

Answer:

a) The mean of the sampling distribution of the sample means is 92.

b) The variance of the sampling distribution of the sample mean is 3.24.

c) The standard error of the sampling distribution of the sample mean is 1.8.

d) 28.77% probability that the sample mean ex-ceeds 93.0 units.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 92, \sigma = 3.6.

a. Find the mean of the sampling distribution of thesample means.

The mean is the same as the mean of the population. So the mean of the sampling distribution of the sample means is 92.

b. Find the variance of the sampling distribution ofthe sample mean.

The standard deviation is s = \frac{\sigma}{\sqrt{n}} = \frac{3.6}{\sqrt{4}} = 1.8

The variance is s^{2} = 1.8^{2} = 3.24

c. Find the standard error of the sampling distribution of the sample mean.

This is the same as the standard deviation of the sample. So the standard error of the sampling distribution of the sample mean is 1.8.

d. What is the probability that the sample mean ex-ceeds 93.0 units?

This is 1 subtracted by the pvalue of Z when X = 93. So

Z = \frac{X - \mu}{s}

Z = \frac{93 - 92}{1.8}

Z = 0.56

Z = 0.56 has a pvalue of 0.7123.

So there is a 1-0.7123 = 0.2877 = 28.77% probability that the sample mean ex-ceeds 93.0 units.

You might be interested in
Please help me with my HW
pentagon [3]
So you can scan it here and it will give you the sotoiun and answers just make sure u show ur workkk good luck
4 0
2 years ago
Read 2 more answers
There were 48 runners to start a race. In the first half of the race, 2/5 of them dropped out. In the second half of the race, 1
12345 [234]

Answer:

SDDAA

Step-by-step explanation:


7 0
3 years ago
Read 2 more answers
The equation for the line of best fit for a data set is y = 2x + 1.5. If the point (1, 4) is in the data set, what is the residu
Andreas93 [3]
A. 0.5 well at least that's the answer in ingenuity.<span />
5 0
2 years ago
Read 2 more answers
HELP ME ASAP PLEASE?!?<br> Classify the following triangle as acute, obtuse, or right.
Lyrx [107]

Answer:

obtuse

Step-by-step explanation:

hope it helps. :)

3 0
3 years ago
-8x-2y=6 in slope form
Harrizon [31]
Perhaps you mean "slope-intercept" form. Solve for y and reduce the fractions.
.. -8x -6 = 2y . . . . . . . . add 2y-6
.. y = -4x -3 . . . . . . . . . divide by 2

Your line in slope-intercept form is
.. y = -4x -3
4 0
3 years ago
Other questions:
  • Determine 4th term in the geometric sequence whose first term is -2 and whose common ration is -5.
    12·1 answer
  • Whats the answer to this problem?
    13·2 answers
  • I need help with this one too
    10·1 answer
  • Find the points of intersection of the graphs involving the following pair of functions.
    6·1 answer
  • I need some help please
    9·1 answer
  • Jacob struggled to solve 0.96 divided by 0.2 so he solved 96 divided by 2 instead. After finding the quotient of 96 divided by 2
    12·1 answer
  • If the original quantity is 10 and the new quantity is 12, what is the percent increase?
    5·1 answer
  • Which number is​ greater, 89 or​ 12.577? How do you​ know?
    12·1 answer
  • Find the length of side a
    7·2 answers
  • An artist creates a​ cone-shaped sculpture for an art exhibit. If the sculpture is 6 feet tall and has a base with a circumferen
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!