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
Katena32 [7]
2 years ago
6

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

ed 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:
defon2 years ago
4 0

Answer:

0.8665 = 86.65% probability that the sample mean would be at least $39000

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}} = 654.72

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}{654.72}

Z = -1.11

Z = -1.11 has a pvalue of 0.1335

1 - 0.1335 = 0.8665

0.8665 = 86.65% probability that the sample mean would be at least $39000

You might be interested in
The courtyard outside East Middle School is in the shape of a rectangle and half-circle.
Nadya [2.5K]

Answer:

The correct option is the third one counting from the top. (5892 m^2)

Step-by-step explanation:

First, we need to remember that:

For a rectangle of length L and width W, the area is:

A = L*W

For a circle of diameter D, the area is:

A = pi*(D/2)^2

Where pi = 3.14

In the image, we can see a rectangle and half a circle, the total area of the image will be equal to the area of the rectangle plus the area of the half circle.

In the image, we can see a rectangle of length L = 100m and width W = 50m

Then the area of the rectangle is:

A = 100m*50m = 5000m^2

And we can see that for the half-circle the diameter is D = 50m

Note that the area of a half-circle is half of the area of a complete circle, then the area of that half-circle is:

A = (1/2)*(3.14*(50m/2)^2) = 981.25 m^2

If we add these two areas we get:

Total area =  5000m^2 + 981.25 m^2 = 5981.25 m^2

If we round it up, we get:

Total area = 5982 m^2

The correct option is the third one counting from the top.

8 0
2 years ago
I really need help with this last problem
gogolik [260]

Answer:


Step-by-step explanation:

a. Profit, p, earned from selling x hats when hat will be sold for $12 each:

p = 12x


b. To recover the cost of making the 200 hats which is $1500, profit, p >= cost:

p = 12x >= 1500

x >= 1500/12 = 12.5

So the minimum number of hats that must be sold = 13


c. New hat price = $15 so p = 15x

p = 15x >= 1500

x >= 1500/15 = 10

So the new minimum = 10 which is 3 fewer.


3 0
3 years ago
Read 2 more answers
A line contains the points (3, 8) and (6, 5). Write the equation of the line in slope-intercept form. Use no spaces in your equa
Artyom0805 [142]
5-8
------ =-3/3=1
6-3
y=1x+b
4 0
3 years ago
Read 2 more answers
A data value that is much higher or much lower then the other values on the data set?
Nitella [24]
A. Outlier is the answer.
5 0
3 years ago
List the given numbers from least to greatest -5, 3.14, 1/4, -3/2, 49
seraphim [82]
-3/2,-5,1/4,3.14,49 hope that helped!
8 0
3 years ago
Other questions:
  • Is 100in more than 3yd 1 ft
    15·2 answers
  • 60+25x=35x+20 write real world situation
    15·2 answers
  • Consider an employee's whose earnings, in dollars, are according to the continuous stream f(t)=5,000e0.1t for t>0, where t is
    14·1 answer
  • Write an expression for the operation described below.
    14·1 answer
  • AT the local zoo, the aquarium can be seen from the Reptile Room and the Amphibian Arena. What is the total area of both rooms a
    11·1 answer
  • There are 32 girls and 17 boys what percent of the class are girls
    15·1 answer
  • The ratio of boys to girls in a class is 4:5, what fraction of the class is boys
    7·2 answers
  • What is the value of x?<br><br> Enter your answer in the box.<br><br> x = <br><br> I NEED HELP ASAP
    13·1 answer
  • Please help me!
    10·1 answer
  • Can someone help me graph y = 2x + 4
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!