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
Dafna1 [17]
3 years ago
8

An Epson inkjet printer ad advertises that the black ink cartridge will provide enough ink for an average of 245 pages. Assume t

hat this claim is accurate and that the standard deviation for this population is 15 pages. A random sample of 33 customers was surveyed about the number of pages they were able to print with their black ink cartridges. What the probability that the sample mean will be 246 pages or more?
Mathematics
1 answer:
Neko [114]3 years ago
4 0

Answer:

35.2% probability that the sample mean will be 246 pages or more

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 245 \sigma = 15, n = 33, s = \frac{15}{\sqrt{33}} = 2.61

What the probability that the sample mean will be 246 pages or more?

This is 1 subtracted by the pvalue of Z when X = 246. So

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

By the Central Limit Theorem

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

Z = \frac{246 - 245}{2.61}

Z = 0.38

Z = 0.38 has a pvalue of 0.6480.

1 - 0.6480 = 0.3520

35.2% probability that the sample mean will be 246 pages or more

You might be interested in
In how many distinct ways can the 11 letters in engineering be arranged
SVEN [57.7K]
The answer is >>> 4 989 600
6 0
3 years ago
June serve 4/9 of the fruit punch . how many litters does she have left?
Zielflug [23.3K]
18- 4/9 = 17 9/9 - 4/9 = 17 5/9 litters
3 0
3 years ago
Here’s another one guys please and thank you
coldgirl [10]

Answer: A. top 0 bottom 6 b. top 0 bottom 0

Step-by-step explanation:

7 0
2 years ago
Write the product in its simplest form
dlinn [17]

Answer:

9u^8v^3

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
6+ (-1/4) = it is making me do 20 characters in brainly​
frez [133]

Answer:

5.75 or 5 3/4

Step-by-step explanation:

6+(-1/4) is the same as 6-1/4. hope this helps!

4 0
3 years ago
Read 2 more answers
Other questions:
  • How do you turn 7 29/80 into a decimal im so confused?
    12·1 answer
  • What is the vertex of the quadratic function below?
    9·1 answer
  • Can someone Help plz!!
    15·1 answer
  • Show cos 20 * cos 40 * cos 80 =1/8
    8·1 answer
  • 6. You are planning a trip. You can go to Phoenix, Las Vegas, San Diego, or Los Angeles. You can
    6·1 answer
  • Troy drives 65 miles west and then drives 72 miles north. How far is he from his starting point?
    6·1 answer
  • Please help quick!!!!!!!!!!
    6·2 answers
  • Find the measure of the angles D, E, and F<br> HELP PLZ
    15·2 answers
  • Based on this graph, is the relationship between number of rows and number of chairs a proportional relationship?
    10·1 answer
  • Which of the following linear equations represents the data chart?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!