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
Plz answer me anyone
Liula [17]

Answer:

1 replaces the question mark.

Step-by-step explanation:

5+8+7=20+1=21

do mark my answer as brainliest

3 0
3 years ago
Read 2 more answers
What are the terms in the expression 7x + 4y + 1?
Sphinxa [80]
There are 3 terms : 7x , 4y, and 1.
a term is separated by any math symbol
examples are =, +, *
7 0
3 years ago
Read 2 more answers
If a auditorium has 850 seats tickets were sold for 816 of the seats of the seats for what percent of the seats were tickets sol
Sonja [21]
It's 96%


816/850 = 0.96, which is 96%

Hope I helped! ( Smiles )
8 0
3 years ago
5 × ( 1 / 3 + 2 / 5 ) = <br><br> write your answer as a mixed number
zheka24 [161]

Answer: the answer is 2 and 1/15

Step-by-step explanation:

7 0
2 years ago
What is the mean to 24 72 46
QveST [7]
The answer would be 46.
4 0
3 years ago
Read 2 more answers
Other questions:
  • In a box of 8 dozen mangoes, 6 are rotten. what is the probability of randomly selecting a mango that is not rotten?
    14·1 answer
  • a lady stole 100 dollars from a cash register. came back in 5mins, and spent 70 dollars worth of merchandise ,and received 30 do
    12·2 answers
  • What is the probability of rolling dice a fair four times and getting in order 1 2 3 4
    10·1 answer
  • Solve the equation by finding the common multiple.
    12·1 answer
  • Someone help me &amp; extra points also brainlest!
    5·1 answer
  • Please answer give it too me now
    5·1 answer
  • Which expression is equal 2n - 6
    9·1 answer
  • If 15% of a number is 24 and 80% of the same number is 128, find 95% of that number.
    10·1 answer
  • The functions it f and g are defined for all real values of x by f(x)=x^2+4ax+a^2 and g(x)=4x-2a where a is a positive constant.
    15·1 answer
  • Graph the function y = 4x4 – 8x2 + 4. Which lists all of the turning points of the graph?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!