The heights of American men aged 18 to 24 are approximately Normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. Only about 5% of young men have heights outside the range​

Answers

Answer 1

(Hope that helps (= The given says the height distribution is normally distributed with the mean height equal to 68 inches. In this case, the bell-shaped curve has a vertical symmetry at 68 inches. This means, half of the mean exceeds 68 inches while the other half has height below 68 inches.

Answer 2

The height range out of which only 5% of the young American men (from age 18 to 24) lie is  [63.35, 72.65] (in inches)

How to get the z scores?

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have

[tex]X \sim N(\mu, \sigma)[/tex]

(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )

then it can be converted to standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

[tex]P(Z \leq z) = P(Z < z) )[/tex]

Also, know that if we look for Z = z in z tables, the p value we get is

[tex]P(Z \leq z) = \rm p \: value[/tex]

For this case, let we take:

X = height of American men from age 18 to 24[a,b] = range of height (the values of X) outside which there lies only 5% of American men.

Then, according to the given data, we have:
[tex]X \sim N(\mu = 68, \sigma = 2.5)[/tex]

where [tex]\mu[/tex] is mean value of X and [tex]\sigma[/tex] is standard deviation of X (both in inches).

Also, we can write:

[tex]P(X < a) + P(X > b) = 5\% = 0.05[/tex]

Since normal distribution is symmetric about its mean, we can take a and b equidistant from the mean, so as to get a symmetric range which makes much more sense than taking an asymmetric range which doesn't comply with the nature of values of X.

Thus, we have:

[tex]\mu - a = b - \mu\\b = 2\mu - a[/tex]

From this result and [tex]P(X < a) + P(X > b) = 5\% = 0.05[/tex], we get:
[tex]P(X < a) + P(X > 2\mu -a) = 0.05[/tex]

Converting X to Z(the standard normal distribution), we get;
[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]

[tex]P(X < a) + P(X > 2\mu -a) = 0.05\\\\P(Z < z = \dfrac{x-\mu}{\sigma} = \dfrac{a-68}{2.5}) + P(Z > \dfrac{2(68) - a - 68}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) + P(Z > \dfrac{68-a}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) + P(Z > -\dfrac{a-68}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) + P(Z \leq \dfrac{a-68}{2.5}) = 0.05 \: \: \: \: (\because P(Z > -k) = P(Z \leq k))\\\\2P(Z < \dfrac{a-68}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) = 0.025[/tex]

Using the z-tables, we get the value of Z for which p-value is 0.025 as

-1.96

Thus, we get:
[tex]\dfrac{a-68}{2.5} = -1.96\\\\a = 68 + (-1.96 \times 2.5)\\a = 63.35[/tex]

Thus, we get: [tex]b = 2\mu - a = 2(68) - 63.35 = 72.65[/tex]

Thus, the range is [a,b] = [63.35, 72.65]

Thus, the height range out of which only 5% of the young American men (from age 18 to 24) lie is  [63.35, 72.65] (in inches)

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Related Questions

Kayla began a science experiment with 18 grams of an unknown solid. During the experiment, the change in the mass of the solid was – 7 grams. What was the mass of the solid at the end of the experiment? To solve the problem, Edna subtracted 18–( – 7) and came up with an answer of 25 grams. Is Edna correct? Why or why not?

Answers

Answer:

No. Enda should have added 18+ (-7) because she needed to add the initial mass and the change in mass.

Step-by-step explanation:

On Monday, you run treadmill for 1/2 hour at x miles per hour. On Tuesday, you walk the same distance on the treadmill, at 2 mph slower, and it takes you 3/4 hour.
How many miles did you run on the treadmill on Monday?

Answers

Distance = rate * time

Let r = rate

 

Distance is the same for both runs,  so:

.5r = D =  3/4(r - 2)

 

Distribute (and convert .5):

2/4r = 3/4r - 3/2

 

Subtract 3/4 r from both sides:

-1/4r = -3/2

 

Multiply both sides by -4 to get a solitary r:

r = -3 * -4 / 2

r = 3 * 2

r = 6 miles per hour

 

.5 hours * 6 mi/hr = 3 miles

 

check:

6 - 2 = 4

3/4 hours * 4 mi/hr = 3 miles

Can someone help me out on this?

Answers

Answer:

<NMP and <QPR

Step-by-step explanation:

Look up corresponding angle examples. these angles are corresponding.

I need help with this geometry

Answers

Answer:

90 degrees

step by step explanation:

LKM moves half way on the blender which is 90 degrees.

el 30% del 40% de 60 es/ 30% of 40% of 60 is​

Answers

Step-by-step explanation:

uiuhhhghjsjsisbsidgurdbridbr d

expand 3(z+3) please help me solve this

Answers

Answer:

3(z+3) = 3z + 9 if thats what your asking

Step-by-step explanation:

Questions 1-5. Bryan invests $500 in an account earning 4% interest that compounds annually. If he makes no additional deposits or withdrawals, how much will be in the account:

After 15 years?

(round to the hundredths place

Answers

Answer:

608.33

Step-by-step explanation:

True or False: Every number has a limited amount of factors, but an unlimited amount of multiples. ​

Answers

Answer:

False

Step-by-step explanation:

0 has unlimited numbers of factors because 0 times everything equals 0. If 0 is not included then the statement is true.

what is the slope of a line that passes through 5,15 and 6,11?

Answers

Answer:

slope is -4, equation is y= -4x + 35

Step-by-step explanation:

 11-15

______

 6-5

-4

____

1

11 = -4(6) + b

b = 35

please answer the questions circled aka: Lillie’s grandmother is making potato salad for a family reunion. She uses three potatoes for each person attending the dinner. If she expects 24 people to attend the reunion, which proportion can be used to solve for p, the number of potatoes? * AWNSER CHOICES ARE ON THE PICTURE and number 2: A 5 lb. package of chicken costs $6.00. What is the cost per pound? *

Answers

Answer:

c

Step-by-step explanation:

the second question 65cent

The answer is B. This is because the answer has to be 24 x 3 and that is what the proportion shows. The second question is $1.20 per pound it is just dividing 6 by 5 to find the unit rate.

Which one?
A or B? ​

Answers

The answer is A

Multiplying an even number of negative terms makes the product positive -4x-6 will be 4x6 so we multiply all of them to get the answer.
3x6x4x6= 432

Which expression is equivalent to-80? O-45 O-4/5 O 45 O 45​

Answers

-4v5i

Step-by-step explanation:

Avas heart rate is 65 beats per minute. If avas heart beat 748,800 times, how many full days would have elapsed

Answers

Answer:

520 full days.

Step-by-step explanation:

Since I'm not that smart I looked up how many minutes are in a day and got a total of 1440 minutes in a day. Then I took the amount of heart beats and divided it by 1440 so we know how many full days. This is what the equation would look like: 748,800/1440.

I hope this helps:)

2x+5/3 = 3x-10
Please can anyone help?

Answers

Answer:

first bring x value together

Step-by-step explanation:

like 2x and 3x together and then take 5/3 to RHS and solve

What is the property demonstrated by the equation (2a)^4 = 16a^4
(^4 indicates an exponent (which is 4))

Answers

Answer:

Ues the site called quetext is helps

Step-by-step explanation:

Multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together. (2a)^4 = 16a^4 is distributive property.

What is Distributive property?

Multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.

If an exponent acts on single term in parentheses, we can distribute the exponent over the term.

(2a)^4

=2^4.a^4

The value of 2^4 is 16, because 2^4=2*2*2*2=16.

=16a^4.

Therefore by distributive property of exponents (2a)^4 = 16a^4.

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What is the solution of 34x+2x=44

Answers

Answer:

x=11/9 hope this helped <3

Step-by-step explanation:

Let's solve your equation step-by-step.

34x+2x=44

Step 1: Simplify both sides of the equation.

34x+2x=44

(34x+2x)=44(Combine Like Terms)

36x=44

36x=44

Step 2: Divide both sides by 36.

-3/4x≤12
what are the steps to solve this??

Answers

Answer:

x≥-16

Step-by-step explanation:

-3/4x≤12

Multiply each side by -4/3, remembering to flip the inequality

-4/3 *-3/4x≥ -4/3 *12

x≥-16

Answer: x ≥ -16

Step-by-step explanation:

Divide both sides by -3/4 to get x alone.

When you divide or multiply both sides by a NEGATIVE, the inequality FLIPS.

-3/4x ≤ 12

Divide both sides by -3/4:

x ≥ -16

Hope this helps!

Casey bought 3/8 pound of plums and 5/12 pound of bananas. How many pounds of fruit did he buy?

Answers

Answer:

19/24 pounds

Step-by-step explanation:

To find the total number of pounds, we should add 3/8 and 5/12. They both have different denominators, so we have to find the least common multiple between 12 and 8. The least common multiple between 12 and 8 is 24. 12 should be multiplied by 2 to get 24 (5 too) and 8 should be multiplied by 3 to get 24 (3 too).

[tex] \frac{3}{8} + \frac{5}{12} [/tex]

[tex] \frac{3 \times 3}{8 \times 3} + \frac{5 \times 2}{12 \times 2} [/tex]

[tex] \frac{9}{24} + \frac{10}{24} [/tex]

[tex] \frac{19}{24} [/tex]

two plus two plus four??

Answers

Answer:

8 lol

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Add from left to right 2+2=4 and then add 4+4 and you get 8

A mobile dealer sells a mobile at a discount of 25% on its marked price and earns a profit of 10%. If the marked price of the mobile is 8800, what will be the cost price of the mobile? 6075​

Answers

Given :

Discount = 25% .

Profit = 10%.

Marked price of mobile = Rs.8800.

Find :

Cost Price of the mobile

Solution :

As we know that, their is no direct relation between Mark price and cost price . so we have to work on selling price of the mobile.

So,

→ MP of mobile = Rs.8800

→ Discount = 25% .

than,

→ SP of mobile = MP * (100 - discount%) / 100

→ SP of mobile = 8800 * (100 - 25) / 100

→ SP of mobile = 88 * 75

→ SP of mobile = Rs.6600 .

Now,

→ SP of mobile = Rs.6600

→ Profit % = 10% .

than,

→ CP of mobile = SP * 100 / (100 + Profit%)

→ CP of mobile = 6600 * 100 / (100 + 10)

→ CP of mobile = (6600 * 100) / 110

→ CP of mobile = 60 * 100

→ CP of mobile = Rs.6000 . (Ans.)

Hence , Cost Price of the mobile is Rs.6000.

I hope it will help you.

Regards.

A percentage is a way to describe a part of a whole. The cost price of the mobile phone is 6,000.

What are Percentages?

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

Let the cost price of the mobile be represented by x.

Given that dealer earn profit of 10% on its cost price, therefore, we can write the selling price of the mobile as,

Selling price = Cost price + Profit

                     = x + 10% of x

                     = 1.10x

Also, given that the mobile dealer sells a mobile at a discount of 25% on its marked price. Therefore, we can write the selling price as,

Selling price = Marked price - Discount

                     = Marked price - 25% of marked price

                     = 8,800 - 25% of 8,800

                     = 8,800 - 0.25(8,800)

                     = 8,800 - 2,200

                     = 6,600

Now, Comparing the sales price we got from above two equation, therefore, the cost price of the mobile can be written as,

1.10x = 6,600

x = 6,600/1.10

x = 6,000

Hence, the cost price of the mobile phone is 6,000.

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DO NOT ANSWER IF YOU DO NOT KNOW, Will give brainliest, like, comment, and 5 points to answer
Each of these is a pair of equivalent ratios, for each pair explain why they are equivalent. 5:1 and 15:3
10.2 and 25.5
198:1,287 and 2:13

Answers

Step-by-step explanation:

5:1 and 15:3 is equivalent because 5 ⋅ 3 = 15, and 1 ⋅ 3 = 3.

10.2 ⋅ 2.5 = 2.5.5 (This wasn't put into a ratio form.)

198:1,287 and 2:13 are equivalent because 198/99 = 2, and 1,287/99 = 13.

Mike and Larry are friends who share the same birthday.They decided to have a birthday party together and their friends. Mike received 21 gifts while Larry received 12 gifts. What is the ratio of gifts for Mike to Larry ​

Answers

Answer:

21:12

Step-by-step explanation:

Answer:

7:4

Step-by-step explanation:

because u simplify 21:12 and u would get 7:4

Which point represents the unit rate?

Answers

Answer:

Point C

Step-by-step explanation:

Unit rate is always how much it is for 1 and point C has a 1 in it's coordinate pair. It isn't point B because point B is not graphed on the line.

Answer:

C.

Step-by-step explanation:

Solve the system of equations -2x+3y=3 x-2y=2

Answers

Answer:

(-12, -7)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

While on spring break, Kayla decided she wanted to go parasailing She was held at a constant angle above the water by a large tow rope attached to the back of the boat. The length of the tow rope is 240 meters. If the angle of the rope keeps Kayla at a horizontal distance of 181 meters away from the boat, how high above the boat is Kayla?

Answers

Answer:

157.6m

Step-by-step explanation:

Given

Horizontal distance = 181m

Length of the rope =240m

To know how high above Kayla was, we will use the Pythagoras theorem.

According to the theorem;

d² = x²+y²

x is the horizontal distance

y is the vertical distance

d is the length of the rope

Substitute

240² = 181²+y²

y² = 240²-181²

y² = 24839

y = √24839

y = 157.6m

Hence the boat is 157.6m above Kayla

A line includes the points (6, 2) and (8, 6). What is its equation in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

y = x −

Answers

Answer:

y=2x-10

Step-by-step explanation:

Hope this helps   (:

I NEED HELP ASAPPPPP

Answers

Answer:

6 decimal places.

Step-by-step explanation:

It's a pretty simple problem. Just simply divide 355 by 113. When you do that you get 3.14159292, which is 6 decimal place accuracy because pi in your problem, is equal to 3.141592654. Then you just count the matching decimal places, which is 6.

The answer is 6. If you divide 355 / 113 it matches pi to the 6 decimal point

Solve for m: 2m + 5-3m = 7

Answers

Answer:

m=-2

Step-by-step explanation:

Answer: m = -2

Step-by-step explanation:

Simplify 2m + 5 - 3m  to -m+ 5

-m + 5 = 7

Regroup terms.

5 - m = 7

Subtract 5 from both sides.

-m = 7 - 5

Simplify 7 - 5 to 2

-m = 2

Multiply both sides by -1

m = -2

Anne works for a company that manufactures liquid dyes for clothing. She currently wants to mix up some 30%-concentrated red dye. She has 66 gallons of 21%-concentrated red dye, as well as plenty of 51%-concentrated red dye. How many gallons of the 51%-concentrated red dye will Anne need to add to the 21%-concentrated red dye to make a batch with a concentration of 30%?

Answers

Answer:

28.29 gallons

Step-by-step explanation:

Given that the available amount of 21%-concentrated red dye= 66 gallons.

Let x gallons of 51%-concentrated red dyes to be mixed with 56 gallons of 21%-concentrated red dye to get 30%-concentrated red dyes.

Total amount of the resulting mixture = 66 + x gallons.

Amount of red dyes in the mixture = (21% of 66) + (51% of x)

To get the resulting mixture as 30%-concentrated red dyes, we have

30% of (66+x) = (21% of 66) + (51% of x)

[tex]\Rightarrow 30(66+x)=21\times66+51x\\ \Rightarrow 30\times 66 +30x= 21\times66+51x\\\Rightarrow 51x-30x=66(30-21)\\\Rightarrow 21x=66\times 9\\\Rightarrow x = 28.29[/tex]

Hence, the amount of 51%-concentration red dyes to be mixed = 28.29 gallons.

Simplify 0.05x + 1.02x.

1.07x
1.7
0.17x

Answers

Answer:

1.07x

Step-by-step explanation:

Since they both have a x, you can simply add .05 + 1.02 to get 1.07x.

Answer:

It is 1.07x (✿◠‿◠)

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