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
Mice21 [21]
3 years ago
6

A research study investigated differences between male and female students. Based on the study results, we can assume the popula

tion mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.05. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. What is the probability that the random sample of 100 male students has a mean GPA greater than 3.42?
Mathematics
1 answer:
oksian1 [2.3K]3 years ago
6 0

Answer: 0.0548

Step-by-step explanation:

Given, A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.05.

Let \overline{X} represents the sample mean GPA for each student.

Then, the probability that the random sample of 100 male students has a mean GPA greater than 3.42:

P(\overline{X}>3.42)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3.42-3.5}{\dfrac{0.5}{\sqrt{100}}})\\\\=P(Z>\dfrac{-0.08}{\dfrac{0.5}{10}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>1.6)\\\\=1-P(Z

hence, the required probability is 0.0548.

You might be interested in
During which time period does Landon's elevation change the fastest? Explain how you know?
bogdanovich [222]
<h3>1. How many inches per minute does London's elevation change between 4 minutes and 8 minutes. </h3>

The question actually asks for the slope of the line that stands for the points (4,3) \ and \ (8,6) why? because the questions tells us that London's elevation changes between 4 minutes and 8 minutes here. Hence, to find the slope of this line we have to use the following formula:

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(4,3) \\ P(x_{2},y_{2})=P(8,6)

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(4,3) \\ P(x_{2},y_{2})=P(8,6) \\ \\ So: \\ \\ m=\frac{6-3}{8-4}=0.75in/min

<em>So London's elevation changes 0.75 inches per minute</em>

<em></em>

<h3>2. During which time period does London's elevation change the fastest?</h3>

The greater the absolute value of the slope of the line the faster London's elevation changes. Since this is a Piecewise function, we must analyze each period.

  • FIRST:

→ Between 0 minutes and 4 minutes the function is constant, so there is no any change here.

→ Between 10 minutes and 14 minutes the function is constant, so there is no any change here.

→ Between 18 minutes and 22 minutes the function is constant, so there is no any change here.

So the solution is not in these parts of the function.

  • SECOND:

→ Between 4 minutes and 10 minutes the function has a positive slope, so there is change here.

In the previous item we calculated the slope between 4 and 8 minutes that is the same slope between 4 and 8 minutes and equals 0.75.

→ Between 14 minutes and 18 minutes the function has a positive slope, so there is change here.

Let's take two points here, say, (16,5) \ and \ (18,3)

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(16,5) \\ P(x_{2},y_{2})=P(18,3) \\ \\ So: \\ \\ m=\frac{3-5}{18-16}=-1 in/min

As you can see, the absolute value here is 1 that is greater than 0.75.

<em>In conclusion, London's elevation changes the fastest between 14 and 18 minutes</em>

7 0
3 years ago
If the price of a gallon of gas was $0.89 in 1984 and was $3.59 in 2014, what was the average rate of change in the price per ga
mylen [45]

Answer:

0.09

Step-by-step explanation:

avg rate of change is:  change in y/ change in x

so it´d be   3.59 - 0.89 / 2014 - 1984

= 2.7/ 30

= 0.09

note:

The slope formula and the average rate of change formula are the same, just written a bit different, so you could also use:

y2 - y1 / x2 - x1

8 0
3 years ago
Help please. Only 20 minutes left.
Tcecarenko [31]

Answer:

-5

Step-by-step explanation:

4 0
2 years ago
the angle of elevation from point c to the top of the cliff is 34°. if point c is 1,000 ft from the base of the cliff, how high
Yanka [14]

Answer:

675 ft (3 s.f.)

Step-by-step explanation:

Please see attached picture for full solution.

7 0
2 years ago
Read 2 more answers
Find u and v only please:
tekilochka [14]

Every two triangles are similar. Therefore the sides of triangles are in proportion.

We have the equations:

1.

\dfrac{3}{5}=\dfrac{3+x}{20}    <em>cross multiply</em>

5(3+x)=(3)(20)      <em>divide both sides by 5</em>

3+x=(3)(4)

3+x=12      <em>subtract 3 from both sides</em>

\boxed{x=9}

--------------------------------------

2.

\dfrac{3}{4}=\dfrac{9}{y}      <em>cross multiply</em>

3y=(4)(9)

3y=36      <em>divide both sides by 3</em>

\boxed{y=12}

------------------------------------------

3.

\dfrac{3}{5}=\dfrac{3+9+u}{60}

\dfrac{3}{5}=\dfrac{12+u}{60}    <em>cross multiply</em>

5(12+u)=(3)(60)      <em>divide both sides by 5</em>

12+u=(3)(12)

12+u=36      <em>subtract 12 from both sides</em>

\boxed{u=24}

----------------------------------------------

4.

\dfrac{3}{4}=\dfrac{24}{v}              <em>cross multiply</em>

3v=(4)(24)

3v=96      <em>divide both sides by 3</em>

\boxed{v=32}

3 0
3 years ago
Other questions:
  • Peter bought 5.65 lbs of hamburger meat to make meatballs write 5.65 as a mixed number
    5·1 answer
  • The volume of a room that is 23 feet in W , 10 feet in D, and 8 feet in H is?​
    14·1 answer
  • 8) y is inversely proportional to x?.<br> When x = 4, y = 3.<br> Find y when x = 5.
    8·1 answer
  • Ted likes to run long distances. He can run
    8·1 answer
  • A line passes through the point and has a slope of -4/3 and (6, -6).
    5·1 answer
  • Can you answer this for me pls i need it ASAP​
    13·1 answer
  • Long addition for integers
    13·2 answers
  • Whats constant of proportanility
    13·1 answer
  • Which is not a true statement about the transformation shown below?
    10·1 answer
  • One root of the equation a(b-c)x^2 + b(c-a)x + c(a-b) = 0 is x=1, find the other root in terms of a, b and c
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!