The heights of women in the USA are normally distributed with a mean of 64 inches and a standard deviation of 3 inches.

Required:
a. A random sample of six women is selected. What is the probability that the sample mean is greater than 63 inches?
b. What is the probability that a randomly selected woman is taller than 66 inches?
c. What is the probability that the mean height of a random sample of 100 women is greater than 66 inches?

Answers

Answer 1

Answer:

(a) 0.2061

(b) 0.2514

(c) 0

Step-by-step explanation:

Let X denote the heights of women in the USA.

It is provided that X follows a normal distribution with a mean of 64 inches and a standard deviation of 3 inches.

(a)

Compute the probability that the sample mean is greater than 63 inches as follows:

[tex]P(\bar X>63)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}>\frac{63-64}{3/\sqrt{6}})\\\\=P(Z>-0.82)\\\\=P(Z<0.82)\\\\=0.20611\\\\\approx 0.2061[/tex]

Thus, the probability that the sample mean is greater than 63 inches is 0.2061.

(b)

Compute the probability that a randomly selected woman is taller than 66 inches as follows:

[tex]P(X>66)=P(\frac{X-\mu}{\sigma}>\frac{66-64}{3})\\\\=P(Z>0.67)\\\\=1-P(Z<0.67)\\\\=1-0.74857\\\\=0.25143\\\\\approx 0.2514[/tex]

Thus, the probability that a randomly selected woman is taller than 66 inches is 0.2514.

(c)

Compute the probability that the mean height of a random sample of 100 women is greater than 66 inches as follows:

[tex]P(\bar X>66)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}>\frac{66-64}{3/\sqrt{100}})\\\\=P(Z>6.67)\\\\\ =0[/tex]

Thus, the probability that the mean height of a random sample of 100 women is greater than 66 inches is 0.


Related Questions

20 less than the sum of eight and a number?

Answers

Answer:

(8 + x) - 20

Step-by-step explanation:

Answer:

The answer is (8 + x) - 20

Step-by-step explanation:

One-fourth of the residents of the Burning Ridge Estates leave their garage doors open when they are away from home. The local chief of police estimates that 5 % of the garages with open doors will have something stolen, but only 1 percent of those closed will have something stolen. If the garage is robbed, what is the probability the doors ware left open

Answers

Answer:

If the garage is robbed, the probability the doors ware left open is 0.625.

Step-by-step explanation:

Denote the events as follows:

X = garage doors open

Y = something is stolen

The information provided is:

P (X) = 0.25

P (Y|X) = 0.05

P (Y|X') = 0.01

Compute probability that the garage is robbed as follows:

[tex]P(Y)=P(Y|X)P(X)+P(Y|X')P(X')\\\\=(0.05\times 0.25)+(0.01\times (1-0.25))\\\\=0.0125+0.0075\\\\=0.02[/tex]

Compute the probability the doors ware left open given that the garage is robbed as follows:

[tex]P(X|Y)=\frac{P(Y|X)P(X)}{P(Y)}\\\\=\frac{0.05\times 0.25}{0.02}\\\\=0.625[/tex]

Thus, if the garage is robbed, the probability the doors ware left open is 0.625.

not sure need help ​

Answers

Answer:

The answer is 504 ft ^3 check my solution

Ty takes 1 hour to read 35 pages, 2 hours to read 70 pages, and 3 hours to read 105 pages.

Answers

Answer: There are 210 pages that ty read in 6 hours.

Step-by-step explanation:

the virus is already 28% loaded if it is loaded at the rate of 12% every 10 minutes how much time do we have before it is 100% loaded .​

Answers

Answer:

You will have 40 mins before 100%

Step-by-step explanation:

The number of minutes taken to completely load is 60 minutes.

Given that, the virus is already 28% loaded if it is loaded at the rate of 12% every 10 minutes.

What is percentage?

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here,

Remaining virus to load =100-28

= 72

The rate of 12% every 10 minutes

Now, 72/12

= 6

So, 6×10 =60 minutes

Therefore, the number of minutes taken to completely load is 60 minutes.

To learn more about the percentage visit:

brainly.com/question/24159063.

#SPJ2

A student wants to use the property
(
x

y
)
(
x
+
y
)
=
(
x
2

y
2
)
to find the product
(
26
)
(
34
)
.
Which statement is true?

Answers

The property is an illustration of difference of two squares

The true statement is [tex]\mathbf{(30 - 4)(30 + 4) = 30^2 -4^2}[/tex]

The property is given as:

[tex]\mathbf{(x - y)(x + y) = x^2 - y^2}[/tex]

The product is given as:

[tex]\mathbf{(26)(34)}[/tex]

Let x - y = 26, and x + y = 34.

So, we have:

[tex]\mathbf{x - y = 26}[/tex]

[tex]\mathbf{x + y = 34}[/tex]

Make x the subject in [tex]\mathbf{x - y = 26}[/tex]

[tex]\mathbf{x = 26 +y}[/tex]

Substitute 26 + y for x in [tex]\mathbf{x + y = 34}[/tex]

[tex]\mathbf{26 + y+ y = 34}[/tex]

[tex]\mathbf{26 + 2y = 34}[/tex]

Subtract 26 from both sides

[tex]\mathbf{2y = 34 -26}[/tex]

[tex]\mathbf{2y = 8}[/tex]

Divide both sides by 2

[tex]\mathbf{y = 4}[/tex]

Substitute 4 for y in [tex]\mathbf{x = 26 +y}[/tex]

[tex]\mathbf{x = 26 + 4}[/tex]

[tex]\mathbf{x = 30}[/tex]

So, we have:

[tex]\mathbf{(x - y)(x + y) = x^2 - y^2}[/tex]

[tex]\mathbf{(30 - 4)(30 + 4) = 30^2 -4^2}[/tex]

Hence, the true statement is [tex]\mathbf{(30 - 4)(30 + 4) = 30^2 -4^2}[/tex]

Read more about difference of two squares at:

https://brainly.com/question/23651973

If r = 18 cm, what is the area of this sector? Express your answer
to the nearest tenth of a centimeter.
A 424.2 cm?
536.2 cm?
1
508.9 cm
834.1 cm?

Answers

Answer:

466

Step-by-step explanation:

nnnnnnnn

This is my question it is in the screen shot please help me.

Answers

4 in = 10.2 cm
7kg = 15.4 lbs
6 gal = 22.7 L
66 ft = 19.8 m

find percent increase
from 24 teachers to 30 teachers ___​

Answers

It’s a 25% increase

What transformation happened to the parent linear function when the m is changed to 3? Parent equation: y=x. New equation y=3x​

Answers

Answer:

Step-by-step explanation:

the funtion was dilated by a factor of 3 since insted or x we have 3x

Amy has 9 cups of flour. If this is 3/4 of the amount she needs to make cake, how many cups does she need?

Answers

ugh sorry no answer.. my answer is wrong..

well it’s actually pretty easy!!
if amy has 9 cups which is 3/4
you need to divide 9 by 3 to find 1/4
which is 3! then 3 x 4 and your answer is 12. 12 cups of flower

When you divide 7.7 by 700, how many decimal places will the quotient have?

Answers

The answer would be 0.011 so there would be three decimal places

NEED HELP DESPERATELY PLEASE IT IS MULTIPLE CHOICE​

Answers

The answer is (-1,-3) because the line passes through that point.

ttttttttttttttttttttttthhhhhhhhhhhhhhhhhhhhhheeeeeeeeeeeeeeeeeeeeerrrrrrrrrrrrrrrrrrrreeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

Step-by-step explanation:

(C)

Sidh is making fruit salad. His recipe calls for 3/4 pound of watermelon. He wants
to make 1/2 of the amount of fruit salad in the recipe. How much watermelon does Sidh need?

Answers

Answer:

3/8

Step-by-step explanation:

3/4 x 1/2 = 3/8

Is the following relation a function?

Yes
or
No

Answers

Answer:

no

Step-by-step explanation:

Answer:

I think that it is yes but not sure

HELP PLZZZ i need it plz

Answers

Pretty messy but hope it helps

Can anyone help it would mean alot im struggling right now

Answers

Answer:

what do you need? ^-^ I can help you

Jamie ordered 200 business cards and paid $23. She ordered 500 business cards and few months later and paid $35. WRITE and SOLVE a linear equation to find the cost to order 700 business cards.

Answers

Find the unit rate of the previous two. use that to plug in 700

simplify 5.42 - 4.987

Answers

Answer:

0.433

Step-by-step explanation:

5.42 - 4.987

Subtract each column of digits starting from right to left.

5.420

- 4.987

If the digit being subtracted is larger than the digit above it then borrow a digit from the next left column.

5.420

- 4.987

Borrow 1 from 5:

4.(10+4)20

- 4.987

4.(14)20

- 4.987

Borrow 1 from 14:

4.(13)(10+2)0

- 4.987

4.(13)(12)0

- 4.987

Borrow 1 from 12:

4.(13)(11)(10+0)

- 4.987

4.(13)(11)(10)

- 4.987

Subtract the second digit from the first:

(10 - 7 = 3):

4.(13)(11)(10)

- 4.987

= 3

(11 - 8 = 3):

4.(13)(11)

- 4.987

= 33

(13 - 9 = 4):

4.(13)

- 4.987

= 433

4.(13)

- 4.987

= .433

(4 - 4 = 0):

4.(13)

- 4.987

= 0.433

What is the equation?

Answers

Answer: y= 2x + 2

Step-by-step explanation:

Yeah she is correct

Show your work please
will give brainliest...
The square of a certain positive number is equal to 2 more than seven-thirds of that number. What is the number?

6
4
3

Answers

Answer:

3

Step-by-step explanation:

x^2=7/3x+2

3^2=7/3(3)+2

9=7+2

9=9

3 is the answer have a great day!!

Pls help with right answers

Answers

Answer:

Ava gives each cat 2 treats. 3 treats are left.

Step-by-step explanation:

15/6 = 2.5

If she wants to split them evenly then she can only give each cat 2 treats. so 2 x 6 = 12 which means that there are 3 treats left

Answer:

She will give 2 cat treats to each cat, with 3 cat treats remaining.

Step-by-step explanation:

Alright, it wants us to find what 15 divided by is is with the remainder.

6 goes into 15,  2 times, resulting in 12.

15 - 12 = 3

This means that she will give 2 cat treats to each cat, with 3 cat treats remaining.

I Hope this Helps!

Have a Great Day (because some other kid tried to ruin mine, but I won't let it affect me)!

Seven more than a number, x, is at most 20

Answers

Answer:

x+7 ≤ 20

Just take it step by step:

seven more than a number is a number plus 7 (x+7)- keep in mind we dont know what the number is so we use x to represent the number.

it then says it's equal to at most 20.

This means that it cant equal anything above 20 since 20 is the max. Therefore, it must be 20 and below that x+7 equals

x+7≤ 20

≤ -this symbol means less than or equal to

Step-by-step explanation:

Which method could be used to prove they are similar?
1.5
3
4.5
Jy

Answers

Answer:

Prove what is similar?????

2:5 =4: ?
Answer

Explain

Answers

2:5 = 4:10 because 4:10 is twice the ratio of 2:5. 2x2 is 4 and 5x2 is 10.

I know m<1 is 55 but I don’t know 2 &3. Please help.

Answers

2 is 55 and 3 is 180-150 so 30

The Jones family has a monthly income of $6,500. The budgeted the following: Retirement savings $700, Emergency savings $550, and Housing expenses $1,300. Which of the following shows the percentage of income used for housing expenses

Answers

Answer:

1867

Step-by-step explanation:

took the test

Find the amount to be paid at the end of eight years that is equivalent to a payment of $400 now and a payment of $300 at the end of four years
(a) if 6% simple interest is earned from the date each payment is made and use a comparison date of right now.
(b) if 6% simple interest is earned from the date each payment is made and use a comparison date of eight years from now.
(c) Explain why the fact you get different answers in parts (a) and (b) does not contradict the fact that equations of value at different times are equiv- alent equations.
(d) Repeat parts (a) and (b) except replace "simple interest" with "compound interest."

Answers

Answer:

A) $964

B) $651.35

C)  The difference in value for part a and part b is due to time factor and the accumulated interest hence it is better to pay $651.35 right now than to pay $964 when you pay $400 now and $300 in four years time

D)  $1016.28 ,  $637.63

Step-by-step explanation:

lets assume the amount to be paid in eight years that is equivalent to payment of $400 now and a payment of $300 at the end of four ( 4 ) years ( FV )

a) since a 6% interest is earned each day of every payment

will use this formula : S = P( 1 + rt )

therefore  $400 paid today will a simple interest of = 400 * 0.06 * 8 = $192

$300 paid at the end of four years will earn a simple interest of = 300*0.06*4 = $72

hence FV = $ ( 400 + 192 ) + $ ( 300 + 72 ) = $964

b) when compared with eight years from now

PV = [tex]\frac{FV}{1+rt}[/tex]  = ($964) / ( 1 + (0.06*8) = $651.35

C) The difference in value for part a and part b is due to time factor and the accumulated interest hence it is better to pay $651.35 right now than to pay $964 when you pay $400 now and $300 in four years time

D) Repeating parts (a) and (b) using compound interest

using the formula : S = P( 1 + r )^t

therefore $400 paid today will have a compound interest of

= 400 ( 1.06)^8 = $637.54

$300 paid at the end of four years will earn a compound interest of

= 300 ( 1.06 ) ^4 = $378.74

hence FV = 637.54 + 378.74 = $1016.28

when compared with eight years from now

= [tex]\frac{FV}{(1+r)^t}[/tex]  = ( 1016.28 ) / ( 1.06 ) ^8    = $637.63

select the correct answer(click the photo)

Answers

Answer:

B.

General Formulas and Concepts:

Order of Operations: BPEMDASEquality Properties

Step-by-step explanation:

Step 1: Define function

f(x) = 8x + 4

Step 2: Prep

Rewrite:                         y = 8x + 4Swap x and y:               x = 8y + 4

Step 3: Find Inverse (Solve for y)

Subtract 4 on both sides:                    x - 4 = 8yDivide both sides by 8:                       (x - 4)/8 = yRewrite:                                                 y = (x - 4)/8Rewrite:                                                f⁻¹(x) = (x - 4)/8
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