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
Orlov [11]
3 years ago
14

Suppose a batch of metal shafts produced in a manufacturing company have a population standard deviation of 1.3 and a mean diame

ter of 208 inches. If 60 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches
Mathematics
1 answer:
lbvjy [14]3 years ago
6 0

Answer:

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

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 problem, we have that:

\mu = 208, \sigma = 1.3, n = 60, s = \frac{1.3}{\sqrt{60}} = 0.1678

What is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Lesser than 207.9.

pvalue of Z when X = 207.9. So

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

By the Central Limit Theorem

Z = \frac{207.9 - 208}{0.1678}

Z = -0.6

Z = -0.6 has a pvalue of 0.2743

2*0.2743 = 0.5486

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

You might be interested in
In the theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to
fiasKO [112]

Step-by-step explanation:

From the statement:

M: is total to be memorized

A(t): the amount memorized.

The key issue is translate this statement as equation "rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized"

memorizing rate is \frac{dA(t)}{dt}.

the amount that is left to be memorized can be expressed as the total minus the amount memorized, that is M-A(t).

So we can write

\frac{dA(t)}{dt}=k(M-A(t))

And that would be the differential equation for A(t).

4 0
3 years ago
A dealer bought an item for $20, sold it for $24, bought it for $25, and sold it for $28. How much profit did she make?
tatiyna
Her profit was around the amount of $7-$52
6 0
3 years ago
Help !! hey pls solve !!
Sunny_sXe [5.5K]

Step-by-step explanation:

3(2x+4)

<em>3</em><em>×</em><em>2x</em><em>+</em><em>3</em><em>×</em><em>4</em>

<em>6</em><em>x</em><em>+</em><em>1</em><em>2</em>

6 0
2 years ago
Read 2 more answers
Lowest common factor of 6 and 12
xxTIMURxx [149]

Answer:

36

Step-by-step explanation:

It's so obvious lollllll

5 0
2 years ago
Read 2 more answers
Find the slope of the line using the points indicated. Then write an equation for the line.
Kryger [21]
The slope of the line is -2/2
5 0
2 years ago
Other questions:
  • ΔBLK is ≅ to Δ What? by the rule of:
    13·1 answer
  • Solve the system of equations using substitution or elimination. Show all work for credit.
    14·1 answer
  • Algebra image below please help I’m struggling I will mark Brainly
    5·1 answer
  • Whats the circumference of a circle if the radius is 4.6
    11·1 answer
  • Perform the indicated operation.<br> 22 6/11 ∙ 1 1/2
    12·1 answer
  • The chemistry teacher decides to use chalk paint to cover a circular portion of a wall in the science lab. If the greatest dista
    10·1 answer
  • Find the volume of the following. Please round your answer to the nearest tenth. Please do not put units. Hint: You need to use
    9·1 answer
  • The difference between x and 5, divided by 6
    9·1 answer
  • Who is the father of modern Biology?<br>​
    6·2 answers
  • A submarine is only allowed to change its depth by rising toward the surface in 60-meters stages. it starts off at (-340) meters
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!