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
lianna [129]
3 years ago
15

Heights of Women. Heights of adult women are distributed normally with a mean of 162 centimeters and a standard deviation of 8 c

entimeters. Use the Table B.3 Areas under the Normal Curve (page 519 of the textbook) to find the indicated quantities: a) The percentage of heights less than 150 centimeters b) The percentage of heights between 160 centimeters and 180 centimeters
Mathematics
1 answer:
Bogdan [553]3 years ago
7 0

Answer:

a) 6.68% of heights less than 150 centimeters

b) 58.65% of heights between 160 centimeters and 180 centimeters

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question, we have that:

\mu = 162, \sigma = 8

a) The percentage of heights less than 150 centimeters

We have to find the pvalue of Z when X = 150. So

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

Z = \frac{150 - 162}{8}

Z = -1.5

Z = -1.5 has a pvalue of 0.0668

6.68% of heights less than 150 centimeters

b) The percentage of heights between 160 centimeters and 180 centimeters

We have to find the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 160.

X = 180

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

Z = \frac{180 - 162}{8}

Z = 2.25

Z = 2.25 has a pvalue of 0.9878

X = 160

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

Z = \frac{160 - 162}{8}

Z = -0.25

Z = -0.25 has a pvalue of 0.4013

0.9878 - 0.4013 = 0.5865

58.65% of heights between 160 centimeters and 180 centimeters

You might be interested in
7. Find the inverse of f(x) = -2x + 10. Please show work.​
Kipish [7]

Answer- y = - x/2 + 5

Step by step - Replace f (x) with y.

Y = - 2x + 10

Interchange the variables.

x= -2y + 10

Solve for y.

Y= x/2 +5

8 0
2 years ago
45 points + brainliest for correct & explained answer :)
devlian [24]
|AD| = 30 - 6 = 24

The triangle ABC and the triangle BDA are similar, therefore:

\dfrac{30}{x}=\dfrac{x}{24}\ \ \ \ |cross\ multiply\\\\x^2=30\cdot24\to x=\sqrt{30\cdot24}\\\\x=\sqrt{5\cdot6\cdot6\cdot4}\\\\x=\sqrt{6^2\cdot4\cdot5}\\\\x=\sqrt{6^2}\cdot\sqrt4\cdot\sqrt5\\\\x=6\cdot2\cdot5\\\\\boxed{x=12\sqrt5}

7 0
3 years ago
Rufus works an average of 46 hours each week. He gets paid $5.70 per
fenix001 [56]
The answer is A. $14,523.60
7 0
2 years ago
PLEASE HELP FAST ILL GIVE 5 STARS!!!!
MArishka [77]
I believe it's Line y=-x+2 and y=3x+1 intersect the y-axis. From what I've gathered, they are parallel lines, and both are set on the y-axis.
8 0
3 years ago
Read 2 more answers
Point R divides in the ratio 1 : 3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of
grandymaker [24]
D -9 because it has a -3 and its going to be the same - sign 
7 0
3 years ago
Read 2 more answers
Other questions:
  • What times what equals 20 but adds up to 19 also ?
    13·1 answer
  • Len tosses a coin three times. the coin shows heads every time. what are the chances the coin shows tails on the next toss?
    6·1 answer
  • Equivalent name for 96
    10·1 answer
  • For retirement, linda invested $4,000 in an account that pays 7% annual interest, compounded quarterly. find the value of his in
    8·1 answer
  • 6 Use the given property of equality to complete each statement.
    12·1 answer
  • Given the following functions, find g(f(x)). f(x) = 2x + 1 g(x) = x2 + 6​
    11·1 answer
  • Someone help me im struggling.
    5·1 answer
  • Describe a way in which the diagram above illustrates the unique line postulate.
    15·1 answer
  • 670.65 which digit is in the tenths place
    15·2 answers
  • At a sale, you purchased a $20 scarf for $15. What<br> was the percent of change?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!