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
Andrej [43]
2 years ago
15

Assume that weights of men are normally distributed with a mean of 170 lb and a standard deviation of 30 lb (approximate values

based on data from the National Health and Nutrition Examination Survey). What percentage of individual men have weights less than 185 lb? If samples of 36 men are randomly selected and the mean weight is computed for each sample, what percentage of the sample means are less than 185 lb?
a. 0.3156
b. 0.2611
c. 0.2312
d. 0.4602
Mathematics
1 answer:
Lubov Fominskaja [6]2 years ago
4 0

Answer:

a) P(X

b) P(\bar X

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Part a

Let X the random variable that represent the weights of men of a population, and for this case we know the distribution for X is given by:

X \sim N(170,30)  

Where \mu=170 and \sigma=30

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability on this way:

P(Z

3) Part b

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

P(\bar X

And using a calculator, excel or the normal standard table we have that:

P(Z

You might be interested in
F(x) = 2x^2+ 5x + 20<br><br> Find f(-9)
8_murik_8 [283]

Answer:

137

Step-by-step explanation:

2(-9)^2+5(-9)+20

2(81)-45+20

162-45+20

117+20

137

8 0
3 years ago
Simplify (3x – 5) + (5x + 1).
Andrej [43]

Answer:

(-2x - 6)

Step-by-step explanation:

The given expression is ( 3x - 5 ) - ( 5x + 1 )

We have to simplify the given expression

First we will open the bracket having negative notation outside.

( 3x - 5 ) - 5x - 1

3x - 5 - 5x - 1

Now we will collect the similar terms together.

3x - 5x - 5 -1

-2x - 6

So the simplified form of the expression is (-2x - 6)

7 0
2 years ago
Read 2 more answers
Which of the following phrases are inequalities?
suter [353]

Answer:

B, C D

Step-by-step explanation:

Inequalities are the "alligators"  <   or >  or the "alligators" with lines  ≤  or ≥

<  less than

>greater than

≤  less than or equal to

≥  greater than or equal to

7 0
3 years ago
Read 2 more answers
the length of a rectagle is 5 in longer than its width. if the perimeter of the rectangle is 58 in, find its length and width
dolphi86 [110]

Answer:

  • Length = 17 inches

  • Width = 12 inches

⠀

Step-by-step explanation:

⠀

As it is given that, the length of a rectangle is 5 in longer than its width and the perimeter of the rectangle is 58 in and we are to find the length and width of the rectangle. So,

⠀

Let us assume the width of the rectangle as x inches and therefore, the length will be (x + 5) inches .

⠀

Now, <u>According to the Question :</u>

⠀

{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}

⠀

{\longrightarrow \qquad { {\sf{2 ( x + 5 + x )= 58 }}}}

⠀

{\longrightarrow \qquad { {\sf{2 ( 2x + 5  )= 58 }}}}

⠀

{\longrightarrow \qquad { {\sf{ 4x + 10= 58 }}}}

⠀

{\longrightarrow \qquad { {\sf{ 4x = 58  - 10}}}}

⠀

{\longrightarrow \qquad { {\sf{ 4x = 48}}}}

⠀

{\longrightarrow \qquad { {\sf{ x =  \dfrac{48}{4} }}}}

⠀

{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 12}} }}} }\:  \:  \bigstar

⠀

Therefore,

  • The width of the rectangle is 12 inches .

⠀

Now, We are to find the length of the rectangle:

{\longrightarrow \qquad{ { \frak{\pmb{Length = x + 5 }}}}}

⠀

{\longrightarrow \qquad{ { \frak{\pmb{Length = 12 + 5 }}}}}

⠀

{\longrightarrow \qquad{ { \frak{\pmb{Length = 17}}}}}

⠀

Therefore,

  • The length of the rectangle is 17 inches .

⠀

8 0
1 year ago
Read 2 more answers
Please help me 5-7g-9=
timofeeve [1]

Answer:

4 - 7g

Step-by-step explanation:

Combine like terms:  5 - 9 - 7g = -4 - 7g (answer)

6 0
2 years ago
Other questions:
  • Can I get some help with this please..
    8·1 answer
  • Apply the distributive property to factor out the greatest common factor of all three terms. {10a - 25 + 5b} =10a−25+5b =
    6·1 answer
  • The Rams won 3 times the number of games as the bears. The lions won 12 more games than the bears. The rams and the lions are bo
    9·1 answer
  • Rick knows that 1 cup of glue weighs 1/18 pound. He has 2/3 pound of glue. How many cups of glue does he have?
    13·1 answer
  • Determine the distance between the following two points. (round to the nearest hundredths)
    12·1 answer
  • Khalid is 56 years old. Cathleen is 6 years older than Brody. The sum of Cathleen's and Brody's ages is half Khalid's age. How o
    15·1 answer
  • HELP PLEASE HELPPPPP
    9·1 answer
  • Lily is making a snack mix for her class.
    5·1 answer
  • Consider the graph of the following quadratic equation
    14·1 answer
  • What is the range of a piecewise function g of x, where part 1 is x squared minus 5 for x less than negative 3 and part 2 is 2 t
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!