IQ is known to follow a normal distribution with a mean of 100 and a standard deviation of 15. If we chose a sample of 10 people, explain in one or two sentences why the distribution would still be considered normal even though the amount of people were under 30.

Complete Question:

a) Is it plausible that X is normally distributed?

b) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 100 min and 125 min?

Answer:

a) It is plausible that X is normally distributed

b) probability that the sample mean courtship time is between 100 min and 125 min is 0.5269

Step-by-step explanation:

a)X denotes the courtship time for the scorpion flies which indicates that is a real - valued random variable, and since normal distribution is a continuous probability distribution for a real valued random variable, it is plausible that X is normally distributed.

b) Probability that the sample mean courtship time is between 100 min and 125 min

[tex]\mu = 120\\n = 50[/tex]

[tex]P(x_{1} < \bar{X} < x_{2} ) = P(z_{2} < \frac{x_{2}- \mu }{SD} ) - P(z_{1} < \frac{x_{2}- \mu }{SD})[/tex]

[tex]SD = \sqrt{\frac{\sigma^{2} }{n} } \\SD = \sqrt{\frac{110^{2} }{50} } \\SD = 15.56[/tex]

[tex]P(100 < \bar{X} <125 ) = P(z_{2} < \frac{125- 120 }{15.56} ) - P(z_{1} < \frac{100- 120 }{15.56})\\P(100 < \bar{X} <125 ) = P(z_{2} < 0.32 ) - P(z_{1} < -1.29)[/tex]

From the probability distribution table:

[tex]P(z_{2} < 0.32 ) = 0.6255\\ P(z_{1} < -1.29) = 0.0986[/tex]

[tex]P(100 < \bar{X} <125 ) = 0.6255 - 0.0986\\P(100 < \bar{X} <125 ) =0.5269[/tex]

Answer:Close to 60 country songs but probably not exactly 60 country songs.

Step-by-step explanation:

Mekala player Jumble has 4 techno songs, 2 country songs, and 3 jazz songs on it.

Represent this songs in ratio format

Ratio of techno songs,to country songs,to jazz songs= 4: 2 : 3

Total number of songs is unknowns ,let it be represented by x

total number of songs is therefore 4 x, 2 x, and 3 x.

Total number of songs that Mekala plans to Listen = 2 70

Then , 4 x + 2 x + 3 x= 270

9 x = 270

Dividing both sides by 9, we get

x = 30

So, Number of techno songs = 4 × 30= 120

Number of country songs = 2 × 30= 60

Number of jazz songs = 3 × 30= 90

Answer:

Close to 60 country songs but probably not exactly 60 country songs

Step-by-step explanation:

Answer:

$36

Step-by-step explanation:

You are going to want to use the simple interest formula for this. The one below is modified for solving the interest earned.

[tex]I = Prt[/tex]

I = interest amount

P = principal amount

r = interest rate (decimal form)

t = time (years)

First, change 4% into a decimal:

4% -> [tex]\frac{4}{100}[/tex] -> 0.04

Now, plug the values into the equation:

[tex]I=300(0.04)(3)[/tex]

[tex]I=36[/tex]

The interest earned is $36

Answer:

Step-by-step explanation:

Find attached the solution

When dividing two fractions, it is important to know to multiply the first fraction by the reciprocal of the second fraction.

Reciprocal means basically a flipped fraction. 2/3 as a reciprocal is 3/2, etc.

1/3 / 1/2= 1/3 x 2/1=2/3

Answer:

(4/3) x 3.14 x (13^3) = 9198.1066666... (repeating decimal)

Step-by-step explanation:

The result of multiplication is: 4/3 x 3.14 x 13³ =9198.11.

Here, we have,

given that,

4/3 x 3.14 x 13³

now, we have to multiply the terms.

so, we get,

4/3 x 3.14 x 13³

=4/3 x 3.14 x 13 x 13 x 13

=4/3 x 3.14 x 2197

=4/3 x 6898.58

=27594.32 /3

=9198.11

Hence, The result of multiplication is: 4/3 x 3.14 x 13³ =9198.11.

To learn more on multiplication click:

brainly.com/question/5992872

#SPJ6

Answer:

8 to 25

Step-by-step explanation:

The total number of lunches sold i

220+120+160 =500

We want the ratio of salads to total lunches

salads: lunches

160:    500

Divide each side by 20

160/20 : 500/20

8:25

Answer:

x,y( 27/13 ,43/13)

Step-by-step explanation:

x=5-4y

•1-2x+5y=16

1-2(5-4y)+5y=16

y=27/13

x=5-4y

x=5-4×27/13

x=-43/13

Answer:

Step-by-step explanation:

Answer:

6 periods

Step-by-step explanation:

The investment is compounded semi-annually which means it is compounded twice in a year. Period of investment is 3 years. So, number of periods compounded is 3 multiplied by 2 that is 6 periods.

Rate would be 8% divided by 2 that is 4%.

Initial investment can be calculated usinf spreadsheet function as =PV(rate,nper, pmt, FV)

Where,

rate is 0.04

nper is 6

pmt is 0

FV is 7,000

So, initial investment is $5,532.20.

It is negative as it is a cash outflow.

Answer:

The probability that Tony removes one yellow, one green ,one blue,and then one more blue tennis ball is 0.0039.

Step-by-step explanation:

We are given that a bucket contains five green tennis balls, two yellow tennis balls, six red tennis balls, and eight blue tennis balls.

As we know that, Probability of an event  =  [tex]\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}[/tex]

Number of green tennis balls = 5

Number of yellow tennis balls = 2

Number of red tennis balls = 6

Number of blue tennis balls = 8

Total number of tennis balls = 5 + 2 + 6 + 8 = 21

{Now it should be notes that Tony removes for tennis balls, without replacement from the bucket means that every time the total number of remaining balls available for selecting will be one less}.

Now, Probability that Tony removes one yellow =  [tex]\frac{2}{21}[/tex]

Probability that Tony removes one green =  [tex]\frac{5}{20}[/tex]

Probability that Tony removes one blue =  [tex]\frac{8}{19}[/tex]

Probability that Tony removes one blue again =  [tex]\frac{7}{18}[/tex]

SO, final probability is =  [tex]\frac{2}{21} \times \frac{5}{20} \times \frac{8}{19} \times \frac{7}{18}[/tex]  

                                      =  [tex]\frac{2}{513}[/tex]

                                      =  0.0039

Answer:

The first one is correct

Step-by-step explanation:

You can multiply the base and perpendicular height to find the area.

Answer:

17

Step-by-step explanation:

300:51*100 =

(300*100):51 =

30000:51 = 588.24

Now we have: 300 is what percent of 51 = 588.24

Question: 300 is what percent of 51?

Percentage solution with steps:

Step 1: We make the assumption that 51 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$x​.

Step 3: From step 1, it follows that $100\%=51$100%=51​.

Step 4: In the same vein, $x\%=300$x%=300​.

Step 5: This gives us a pair of simple equations:

$100\%=51(1)$100%=51(1)​.

$x\%=300(2)$x%=300(2)​.

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

$\frac{100\%}{x\%}=\frac{51}{300}$

100%

x%​=

51

300​​

Step 7: Taking the inverse (or reciprocal) of both sides yields

$\frac{x\%}{100\%}=\frac{300}{51}$

x%

100%​=

300

51​​

$\Rightarrow x=588.24\%$⇒x=588.24%​

Therefore, 17% of 300 is 51

Answer:

Answer 17%

Step-by-step explanation:

Solution for 300 is what percent of 51:

300:51*100 =

(300*100):51 =

30000:51 = 588.24

588.24 as a percentage is 17%

Answer: C.

Simple random sampling

Step-by-step explanation:

A simple random sample in statistics, is a subset of individuals chosen from a larger set. Each individual is chosen randomly and entirely by chance, such that each individual has the same probability for the entire larger set.

Answer:

C

Step-by-step explanation:

The computer randomly selects 500 names without any bias, Thus, it is simple random sampling because each name has equal chance of getting selected.

Answer:

19

Step-by-step explanation:

if x=3

Answer:

x = 2

Answer:

116

Step-by-step explanation: You would have to split the figure into a square and a triangle as you can see in the picture. You then find the area of each figure.

Area of Square : 8 * 8 = 64

Area of Triangle : 8 * 13 /2 = 52

Then, you add the areas of both figures together to get 116.

Answer:

Step-by-step explanation:

hello :

let: A = 3√16+√-9

16=4²   and  -9 = 9i² =(3i)²   .... ( i² = -1)

√16 =√4² = 4     and  √-9 = √9i²= √(3i)² ± 3i

A= 12  ± 3i

Answer: The third option.

Step-by-step explanation:

This is an equation because it has an equals sign that can be solved for, making it an equation.

Answer:

x + 3 = 12

Step-by-step explanation:

This is an equation because it contains an equal sign, if it does not contain an equal sign then it is an expression.

Answer:

(x+5y)(x+6y)

Step-by-step explanation:

Answer:

The answer is 1 : 3 : 2

Step-by-step explanation:

First, you have to make them into same unit by converting it into km or m :

1 km = 1000 m

0.007 km = 7 m

0.021 km = 21 m

7 : 21 : 14

OR

14 m = 0.014 km

Then you can simplify it by 7 :

m,

7 : 21 : 14

= 1 : 3 : 2

OR

km,

0.007 : 0.021 : 0.014

= 0.001 : 0.003 : 0.002

= 1 : 3 : 2

(take note: in ratio, it is better to put it in whole number form rather than decimal form)

Answer:

its D the last one i just took the assignment

Step-by-step explanation:

Answer:

The answer is D.

Step-by-step explanation:

I took the assignment.

Answer:

The correct answer is 52 squats.

Step-by-step explanation:

An exercise routine requires 24 crunches for every 16 squats.

Therefore the routine would require 1 crunch for every [tex]\frac{16}{24}[/tex] squats.

And by the use of unitary method, the routine would require 78 crunches for every [tex]\frac{16}{24}[/tex] × 78 squats = 52 squats.

Thus for every 78 crunches attempted, the exercise routine would requires 52 squats to be done.

Answer:

Length in feet is equal to [tex]\frac{2P}{6.5}[/tex], where P is the perimeter

Step-by-step explanation:

Let the width (W) of the yard be "X"

[tex]W = w[/tex]

Then the length(L) of the yard will be

[tex]2\frac{1}{4} * w[/tex]

[tex]L = \frac{9}{4} *w[/tex]

The perimeter of the yard will be equal to the sum of twice the length and width of the yard

Thus,

[tex]P = 2 W + 2L\\[/tex]

Substituting the given values in above equation, we get -

[tex]P = 2 w + 2 (\frac{9}{4})w\\P = 2w + 4.5 w\\P = 6.5w[/tex]

Thus, width in terms of perimeter is equal to

[tex]w = \frac{P}{6.5}[/tex]

Length in feet is equal to [tex]\frac{2P}{6.5}[/tex]

Given:

Desmond deposits $ 50 monthly.

Yearly he deposits = $50×12 = $ 600

Rate of interest compounded monthly = 4.7%

To find the amount he will receive after 10 years and the rate of change the value of his account after 10 years.

Formula

[tex]A = P(1+\frac{r}{(n)(100)} )^{nt}[/tex]

where,

A be the final amount

P be the principal

r be the rate of interest

t be the time and

n be the number of times the interest is compounded.

Now,

Taking,

P = 600, r = 4.7, n = 12, t = 10 we get,

[tex]A = 600(1+\frac{4.7}{(12)(100)}) ^{(12)(10)}[/tex]

or, [tex]A = 600(1.0039)^{120}[/tex]

or, [tex]A = 959.1[/tex]

Now,

At starting he has $ 600

At the end of 10 years he will be having $ 959.1

So,

The amount of change in his account = $ (959.1-600) = $ 359.1

Therefore the rate of change = [tex](\frac{359.1}{600} )(100) %[/tex]

= 59.85%

Hence,

a) His account will contain $ 959.1 after 10 years.

b) The rate of change in his account is 59.85% after 10 years.

Answer:

3.4

Step-by-step explanation:

3.4+3.4= 6.8

10.2-6.8=3.4

Answer:

The best interpretation of one of the values of the function is that the rate  increases by 12% each day.

Step-by-step explanation:

Given:

F(x)=245(1.12)^x

To Find:

statement is the best interpretation of one of the values of the function

Solution:

Depending upon the values given the statement can be developed

As the function is itself the exponential growth structure ,

In this the statement ,Growth can be significantly depends on all factor

Such as time period initial value and rate.

But here the formula is simplified as ,

[tex]P=A(1+r)^t[/tex]

Here A= initial value r=rate and t =time period

Here A=245 and 1+r=1.12

i.e r=0.12 i.e 12%

Hence the rate give the best interpretation and more information about the function and scenario.

The function f(x)=245(1.12)^x models the exponential growth of bacteria in a sample over x days, with the base 245 being the initial number and 1.12 representing the daily growth rate.

The function f(x)=245(1.12)^x describes the exponential growth of bacteria, where the base number (245) represents the initial amount of bacteria and 1.12 indicates the growth rate per day.

For example, if we want to determine the number of bacteria at the end of the first day (x=1), we substitute 1 into the function to get f(1)=245(1.12)^1, which would give us the total number of bacteria at the end of day one.

The exponent x stands for the number of days and shows how the population grows at an increasing rate over time, which is a signature characteristic of an exponential function in a context like bacterial growth.

Answer:

[tex](9 - 4) \\ ( {3}^{2} - {2}^{2}) \\ (3 - 2)(3 + 2) \\ 1 \times 5 = 5 [/tex]

hope this helps you.

Answer:

$2

Step-by-step explanation:

She earns 5%  of $40 each year. To find how much she makes in 1 year, multiply 5% and 40

40*5%

Convert 5% to a decimal by dividing by 100

5%/100=0.05

40*0.05=2

So, in one year, the account earns $2 in interest