Determine the location of a' after the image<br> has been dilated with a scale factor of 2

According to a recent Census Bureau report, 12.7% of Americans live below the poverty level. Suppose you plan to sample at rando

larisa [96]

Answer:

a) $P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928$

b) $P(X \leq 10) = 0.2614$

c) $(1-0.127)^7 (0.127) =0.0491$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=100, p=0.127)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

a. What is the probability that you count exactly 10 in poverty?

For this case we want this probability P(X=10)

$P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928$

b. What is the probability that you count 10 or less in poverty? .2614

For this case we want this probability $P(X=\leq10)$

$P(X\leq10)=P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)$

And we can find the individual probabilities like this:

$P(X=0)=(100C0)(0.127)^{0} (1-0.127)^{100-0}=1.263x10^{-6}$

$P(X=1)=(100C1)(0.127)^{1} (1-0.127)^{100-1}=1.837x10^{-5}$

$P(X=2)=(100C2)(0.127)^{2} (1-0.127)^{100-2}=0.000132$

$P(X=3)=(100C3)(0.127)^{3} (1-0.127)^{100-3}=0.000629$

$P(X=4)=(100C4)(0.127)^{4} (1-0.127)^{100-4}=0.00222$

$P(X=5)=(100C5)(0.127)^{5} (1-0.127)^{100-5}=0.00620$

$P(X=6)=(100C6)(0.127)^{6} (1-0.127)^{100-6}=0.0143$

$P(X=7)=(100C7)(0.127)^{7} (1-0.127)^{100-7}=0.0279$

$P(X=8)=(100C8)(0.127)^{8} (1-0.127)^{100-8}=0.0471$

$P(X=9)=(100C9)(0.127)^{9} (1-0.127)^{100-9}=0.0701$

$P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928$

And then repplacing we got:

$P(X \leq 10) = 0.2614$

c. What is the probability that you start taking the random sample and you find the first person in poverty on the 8th person selected? .0491

For this case we need after 7 people , 1 in poverty so we can find this probability like this:

$(1-0.127)^7 (0.127) =0.0491$

7 0

3 years ago

HELP ASAP !!

Aleks [24]

Answer:

Step-by-step explanation:

total money = $2.25 = 225 cents

types of denomination in coins or cents are dimes and nickels

dime = 10 cents , nickel = 5 cents

twice of dimes to nickels

let no of dimes = x and no of nickels = y

our equation

10x + 5y = 225

x = 2y

10(2y) + 5y = 225

20y +5y = 225

25 y = 225

y=9

x =2y 2x9 = 18

so the number of dimes = 18 and nickels = 9

cross verification:

10x18 + 5x9 = 180 +45 = 225

6 0

3 years ago

Help! Select the correct answer.<br> Graph the following system of inequalities. WILL GIVE BRAINLY!!

Sindrei [870]

Answer:

w is the correct answer

Step-by-step explanation:

$y \leqslant \frac{1}{3} x - 2$

If we choose the point (3, 0), we obtain

0 <= -1, which is not true. So we shade the region to the left of x = 4 (which is a dashed vertical line) and below

y = (1/3)x - 2 (which is a solid line).

8 0

3 years ago

Please help me to solve these questions as soon as possible. Thank you

Mama L [17]

Answer:

1) B, 48

2) C. 180=2x2x3x15

Step-by-step explanation:

8 0

3 years ago

A community college student interviews everyone in his own statistics class to determine who owns a car. Identify which sampling

sladkih [1.3K]

The answer is soo easy it’s obviously B

6 0

3 years ago

Determine the location of a' after the image has been dilated with a scale factor of 2