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
Sidana [21]
2 years ago
14

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 Ď = 0. 5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. Find the interval that contains 95. 44 percent of the sample means for male students.
Mathematics
1 answer:
garri49 [273]2 years ago
7 0

Using the <u>normal distribution and the central limit theorem</u>, it is found that the interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

  • It 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, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

In this problem:

  • The mean is of \mu = 3.5.
  • The standard deviation is of \sigma = 0.5.
  • Sample of 100, hence n = 100, s = \frac{0.5}{\sqrt{100}} = 0.05

The interval that contains 95.44% of the sample means for male students is <u>between Z = -2 and Z = 2</u>, as the subtraction of their p-values is 0.9544, hence:

Z = -2:

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

By the Central Limit Theorem

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

-2 = \frac{X - 3.5}{0.05}

X - 3.5 = -0.1

X = 3.4

Z = 2:

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

2 = \frac{X - 3.5}{0.05}

X - 3.5 = 0.1

X = 3.6

The interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213

You might be interested in
Please say this answer fast now​
ludmilkaskok [199]

Answer:

4 is the correct answer of the question

7 0
3 years ago
What is the slope of the equation -4x-7y=-14
castortr0y [4]
The answer to your question is precisely 99
3 0
2 years ago
Find the payment necessary to amortize a 6.3% loan of 7500 compounded semiannually, with 6 semiannual payments. Find the payment
Lorico [155]

Answer:

Semiannual payment = $ 1391.37

Total payment = $ 8348.22

Interest paid =  $ 848.22

Step-by-step explanation:

Since, the semiannual payment formula of a loan,

P=\frac{PV(\frac{r}{2})}{1-(1+\frac{r}{2})^{-n}}

Where,

PV = present value of the loan,

n = number of semiannual payments,

r = annual rate,

Here, PV = 7500, r = 6.3% =0.063, n = 6,

By substituting the value,

The semiannual payment would be,

P=\frac{7500(\frac{0.063}{2})}{1-(1+\frac{0.063}{2})^{-6}}

\approx \$ 1391.37

Also, total payment = semiannual payment × total semiannual periods

= 1391.37 × 6

= $ 8348.22,

Also, the interest paid = total payment - present value

= 8348.22 - 7500

= $ 848.22

6 0
3 years ago
Determine the value of x, using the following transversal. The value of x is
madam [21]

Answer:

  • x = -10

Step-by-step explanation:

  • x + 75 + x + 125 = 180 as supplementary (same side interior angles)
  • 2x + 200 = 180
  • 2x = -20
  • x = -10
3 0
2 years ago
Read 2 more answers
10<br> 10<br> 5<br> -10<br> 0<br> 10<br> -10<br> 0<br> 10<br> 10<br> 1.5<br> 10<br> 10<br> -10
Archy [21]

Answer:

???????................ .mm

8 0
3 years ago
Read 2 more answers
Other questions:
  • Given f(x) =<br> + 2, find f(0)
    9·1 answer
  • Can you please answer my question 53(I will put on you brainliest)
    5·1 answer
  • How to find 1/2 of 3/4?
    15·2 answers
  • The number of times a particular value a car in a data set is called what ​
    12·1 answer
  • Classify the area of a circle with a radius of 0.75 centimeter seems as either rational or irrational
    11·1 answer
  • What is the value of y for the line when x=-4
    12·1 answer
  • Read the caption please! Thank you :)) please help!
    10·1 answer
  • How do I turn 93.75 into a fraction? :)
    14·2 answers
  • Can someone help me with this circle geometry question ty
    13·1 answer
  • Please help me pleaseeee
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!