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
coldgirl [10]
2 years ago
12

Consider a normal distribution curve where the middle 85 % of the area under the curve lies above the interval ( 8 , 14 ). Use t

his information to find the mean, \mu , and the standard deviation, \sigma , of the distribution.
Mathematics
1 answer:
NeTakaya2 years ago
7 0

Answer:

\mu = 11

\sigma = 2.08

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Middle 85%.

Values of X when Z has a pvalue of 0.5 - 0.85/2 = 0.075 to 0.5 + 0.85/2 = 0.925

Above the interval (8,14)

This means that when Z has a pvalue of 0.075, X = 8. So when Z = -1.44, X = 8. So

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

-1.44 = \frac{8 - \mu}{\sigma}

8 - \mu = -1.44\sigma

\mu = 8 + 1.44\sigma

Also, when X = 14, Z has a pvalue of 0.925, so when X = 8, Z = 1.44

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

1.44 = \frac{14 - \mu}{\sigma}

14 - \mu = 1.44\sigma

1.44\sigma = 14 - \mu

Replacing in the first equation

\mu = 8 + 1.44\sigma

\mu = 8 + 14 - \mu

2\mu = 22

\mu = \frac{22}{2}

\mu = 11

Standard deviation:

1.44\sigma = 14 - \mu

1.44\sigma = 14 - 11

\sigma = \frac{3}{1.44}

\sigma = 2.08

You might be interested in
(4+2x)+(3+1x) simplify!
larisa [96]

Answer:

3x+7

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What is the unit rate of a line that goes through the points (3,1)?
Ket [755]

Answer:

3.

Step-by-step explanation:

3 divided by 1 equals 3.

Please mark me brainliest I need it!!!

7 0
3 years ago
Five years ago, the tree you planted measured 4 meters 9 decimeters tall. Today that tree measures 6 meters, 1 decimeter. How mu
Gnesinka [82]

Answer: 1.2metres

Step-by-step explanation:

Five years ago, tree was 4.9m

Today, tree is 6.1m

Subtract 4.9m from 6.1m

Tree has grown by 1.2m

7 0
3 years ago
Identify the digit with the given place value in number 173.514 hundredths
Llana [10]

Answer: We are given the number 173.514

Each of the digits in this number has the following place value:

\begin{gathered} 1\rightarrow\text{ Hundreds} \\ 7\rightarrow\text{ Tens} \\ 3\rightarrow\text{ Ones} \\ \text{.}\rightarrow\text{  Decimal Point} \\ 5\rightarrow\text{ Tenth} \\ 1\rightarrow\text{  Hundreth} \\ 4\rightarrow\text{  Thousandth} \end{gathered}

Secondly, We have to identify the numbers in digit 185.712

\begin{gathered} 1\rightarrow\text{ Thousand} \\ 8\rightarrow\text{ Hundred} \\ 5\rightarrow\text{ Tens} \\ \text{. Decimal point} \\ 7\text{ }\rightarrow\text{Thenth} \\ 1\rightarrow\text{ Hundreth} \\ 2\text{ }\rightarrow\text{ Thousandth} \\  \end{gathered}

5 0
1 year ago
PLEASE HELP !!! The height of a rectangle is twice the width and the area is 32. Find the dimensions.
Helen [10]

Answer:

The rectangle has a width of 4 and a height of 8

Step-by-step explanation:

Let the height of the rectangle be H and the width be W.

We know the height of the rectangle is twice the width, so:

H = 2W

The area of a rectangle, A, is given by A = W * H, so in this case:

32 = W * 2W

32 = 2W²

W² = 16

W = 4

Knowing that the width is 4, the height must be 8. This gives us an area of 32.

8 0
3 years ago
Read 2 more answers
Other questions:
  • Factorise 2xy-2x+6-6y
    11·1 answer
  • I need help on this question
    15·1 answer
  • Given that F(x) =x^2+2, evaluate F(2)
    13·1 answer
  • Complete factor of 12m+60
    11·1 answer
  • 12-w=1 solve for w help me please
    15·1 answer
  • The probability of choosing a green ball out of a box of balls is 2/9. What are the odds in favor of choosing a green ball?
    13·1 answer
  • GUYS HELP please!!!
    15·2 answers
  • Once a commercial plane reaches the desired altitude, the pilot often travels at cruising speed. On average, the cruising speed
    14·1 answer
  • A. -2x + y = -2
    10·1 answer
  • A rectangle with a length of 28 and perimeter of 64 what is the width and what is the area
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!