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
Arturiano [62]
2 years ago
11

Need help

Mathematics
1 answer:
aleksandr82 [10.1K]2 years ago
8 0

Using the normal distribution, the probabilities are given as follows:

a. 0.4602 = 46.02%.

b. 0.281 = 28.1%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

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

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, 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}}.

The parameters are given as follows:

\mu = 959, \sigma = 263, n = 37, s = \frac{263}{\sqrt{37}} = 43.24

Item a:

The probability is <u>one subtracted by the p-value of Z when X = 984</u>, hence:

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

Z = \frac{984 - 959}{263}

Z = 0.1

Z = 0.1 has a p-value of 0.5398.

1 - 0.5398 = 0.4602.

Item b:

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

By the Central Limit Theorem:

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

Z = \frac{984 - 959}{43.24}

Z = 0.58

Z = 0.58 has a p-value of 0.7190.

1 - 0.719 = 0.281.

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

You might be interested in
Gerry is knitting a scarf for a friend. She knits a gauge swatch which measures 4 in. by 4 in. If the square is 30 stitches wide
LiRa [457]

Answer:

<u>Gerry will need to knit 135 stitches wide and 351 rows long for make a scarf that is 18 inches wide and 36 inches long.</u>

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Measures of the gauge swatch = 4 inches * 4 inches

Number of stitches wide of the gauge swatch = 30

Number of rows long of the gauge swatch = 39

2. How many stitches wide will she need to knit in order to make a scarf that is 18 inches wide and 36 inches long?

Using Rule of Three Simple we can found that value, this way;

Number of stitches wide for 18 inches wide = (18 * 30)/4

Number of stitches wide for 18 inches wide = 540/4 = 135

<u>Gerry will need to knit 135 stitches wide for make a scarf that is 18 inches wide.</u>

We can found the same way, the rows long:

Number of rows long for 36 inches long = (36 * 39)/4

Number of rows long for 36 inches long = 1,404/4 = 351

<u>Gerry will need to knit 351 rows long for make a scarf that is 36 inches long.</u>

8 0
3 years ago
14-
Vaselesa [24]

Answer: You need 27 more dollars.

Step-by-step explanation: This is because for this problem, you need to subtract 65 from 38 to get 27

4 0
2 years ago
A person has a body fat percent of 15.2% and weighs 185 pounds. How many poundsof his weight is made up of fat? Round your answe
puteri [66]

We can find the 15.2% of 185 pounds by dividing the weight by 15.2% in its decimal form:

185(15.2\%)=185(0.152)=27.7\text{pounds}

therefore, there are 27.7 pounds of fat

3 0
1 year ago
What is the place vaule of the 7 in 9.357
kumpel [21]

The 7 is in the Ones place

4 0
3 years ago
Read 2 more answers
Simplify this equation <br> Thanks a lot!!!
den301095 [7]

Answer:

-1

Step-by-step explanation:

We need to simplify the given expression . The given expression is ,

\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}

Here we can see that the power of the both exponent is same that is (2n+1) . Recall the property of exponents ,

\bf\implies a^m \times b^m = (ab)^m

Using this property , we have ,

\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}

This can be written as ,

\rm\implies\{( 2 \sqrt6 +5) ( 2\sqrt6 - 5)\}^{2n-1}

Simplifying using ( a+b)(a-b) = a² - b² ,

\rm\implies\{( 2 \sqrt6)^2 -5^2 \}^{2n-1}\\\\\rm\implies ( 24 - 25)^{2n-1}

Subtracting the numbers inside the brackets ,

\rm\implies (-1)^{2n - 1 }

Now we know that every odd number is in the form of 2n -1 , where n is any integer. Therefore , the <u>power is odd</u> .

Since the base is (-1) , for even power it is 1 and for odd power it is -1 . Therefore the final answer is ,

\rm\implies\boxed{\quad \red{ -1 }\quad }

<u>Hence </u><u>the</u><u> </u><u>required</u><u> answer</u><u> is</u><u> </u><u>(</u><u>-</u><u>1</u><u>)</u><u> </u><u>.</u>

4 0
3 years ago
Other questions:
  • Just say answer, no need to explain! THANKSSS!
    5·1 answer
  • A bookstore orders 200 books. The books are packaged in boxes that hold 24 books each. All the boxes the bookstore receives are
    13·1 answer
  • Calculate the average rate of change for the given function, from x = 8 to x = 5.
    12·2 answers
  • Explain how complex fractions can be used to solve problems involving ratios
    15·2 answers
  • Nov 18, 10:52:11 PM
    8·1 answer
  • Point T is on line segment SU. Given ST = 4x – 4, TU = 4x – 10, and
    8·1 answer
  • Please help I’ll mark u :(:
    13·2 answers
  • Sam and Martha had a total bill (Including tax) of $29 32 at The Spaghetti House restaurant They also purchaued 2 shirts for $19
    11·1 answer
  • 1. Find the percent of the given quantity using any method: 40% of 320
    13·2 answers
  • How to represent 5 rational numbers on line. the numbers should be of form p/q where p or q should be a taxicab number. the frac
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!