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
jonny [76]
2 years ago
10

g Annual starting salaries in a certain region of the U. S. for college graduates with an engineering major are normally distrib

uted with mean $39725 and standard deviation $7320. Suppose a school takes a sample of 125 such graduates and records the annual starting salary of each. The probability that the sample mean would be at least $39000 is about
Mathematics
1 answer:
algol132 years ago
4 0

Answer:

The probability that the sample mean would be at least $39000 is of 0.8665 = 86.65%.

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 normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, 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.

Mean $39725 and standard deviation $7320.

This means that \mu = 39725, \sigma = 7320

Sample of 125

This means that n = 125, s = \frac{7320}{\sqrt{125}}

The probability that the sample mean would be at least $39000 is about?

This is 1 subtracted by the pvalue of Z when X = 39000. So

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

By the Central Limit Theorem

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

Z = \frac{39000 - 39725}{\frac{7320}{\sqrt{125}}}

Z = -1.11

Z = -1.11 has a pvalue of 0.1335

1 - 0.1335 = 0.8665

The probability that the sample mean would be at least $39000 is of 0.8665 = 86.65%.

You might be interested in
PLEASE HELP ME WITH THESE
elena-s [515]
You have to take the 2 divided by 12. And 12 divided by 2 is 6. So the answer is 6
7 0
2 years ago
Can y'all help me pls ​
guajiro [1.7K]

Answer:

The change in delta x would be 0 in the second option because the change is exactly the same.

8 0
3 years ago
Read 2 more answers
What is three times as long of 20 square meters
Stolb23 [73]
Three times as long of 20 square meters would be 60

you can do 20×3 to get 60.
6 0
3 years ago
Simplify 6x + 8 / 4x + 4
Mars2501 [29]

(6x + 8) / (4x + 4)
(3x +4)   2(x  1)

2(3x + 4)  4(x +1) 
3 0
3 years ago
Will i pass 6th grade with these grades?
kobusy [5.1K]

My question is, “is it over due work or low grades?”

8 0
3 years ago
Read 2 more answers
Other questions:
  • Which number line represent the solution to |x+4|=2
    13·2 answers
  • 1. Find the value of x in the figure below. Show all steps. (Left)
    10·2 answers
  • Laura got a discount of 100 dollars on her purchase of a 5775 bed.What is the percent of decrease?
    8·1 answer
  • How are unit circle and trigonometric functions related?
    15·1 answer
  • Which of the follows graphs show a pair of lines that represent the equations with a solution (-4,3)
    9·2 answers
  • 3 x (1 3/8 + 1/2<br> 3/8 and 1/2 is a fraction <br> Please hurry 5th math is a nightmare!!
    14·1 answer
  • Mae has a number cube with 6 sides that are numbered 1 through 6. What is the probability that Mae will roll an odd number?
    8·1 answer
  • Find the slope please using the formula
    13·1 answer
  • DIRECTIONS: Use this information to answer Parts A and B. Rosa earns $12.25 per hour working at an ice-cream shop. Part A Write
    10·1 answer
  • Four boxes of cookies were sold to a family of five each box contains 12 cookies if each family member ate 2 cookies from each b
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!