In a sample of 1000 U.S. adults. 217 think that most celebrities are good role models. Two U.S. adults are selected from this sample without replacement.


Find the probability that both adults think most celebrities are good role models

(Round to three decimal places as needed.)


Find the probability that neither adult thinks most celebrities are good role models

(Round to three decimal places as needed.)


Find the probability that at least one of the two adults thinks most celebrities are good role models

(Round to three decimal places as needed)

Answer:

(a) 0.047

(b) 0.613

(c) 0.387

Step-by-step explanation:

In a sample of 1000 U.S. adults 217 think that most celebrities are good role models.

The proportion of U.S. adults who think that most celebrities are good role models is, p = 0.217.

Two U.S. adults are selected from this sample without replacement.

Let X denote the number of U.S. adults who think that most celebrities are good role models.

Both the individuals are independent of each other.

The random variable X follows a binomial distribution with parameters n = 2 and p = 0.217.

The probability mass function of X is:

[tex]P(X=x)={2\choose x}(0.217)^{x}(1-0.217)^{2-x};x=0,1,2[/tex]

(a)

Compute the probability that both adults think most celebrities are good role models as follows:

[tex]P(X=2)={2\choose 2}(0.217)^{2}(1-0.217)^{2-2}\\=1\times 0.047089\times 1\\=0.047[/tex]

Thus, the probability that both adults think most celebrities are good role models is 0.047.

(b)

Compute the probability that neither adult thinks most celebrities are good role models as follows:

[tex]P(X=0)={2\choose 0}(0.217)^{0}(1-0.217)^{2-0}\\=1\times 1\times 0.613089\\=0.613[/tex]

Thus, the probability that neither adult thinks most celebrities are good role models is 0.613.

(c)

Compute the probability that at least one of the two adults thinks most celebrities are good role models  as follows:

[tex]P(X\geq 1)=1-P(X<1)\\=1-P(X=0)\\=1-0.613\\=0.387[/tex]

Thus, the probability that at least one of the two adults thinks most celebrities are good role models  is 0.387

Translate the sentence into an equation.
Seven times the sum of a number and 2 is 6.
Use the variable y for the unknown number.

I need help please thanks
find x when y = 18, if y = 9 when x = 8
ASAP PLEASE

Seventeen less than a number
is negative two. What is that
number?

Write the following as an inequality. 9 is greater than x, and 3 is less than x Use x only once in your inequality. also please understand that two people need to answer the question for me to give brainiest, and yes once two people answer I will choose brainliest for whoever is correct

B^2 + 11b + 18 ( Factor the question)
Help please!

SOMEONE PLEASE HELP ILL GIVE BRAINLIEST

The table shows the unit prices (per pound) of tomatoes
at different stores.
Store
Tomato Unit Prices
Jamal needs to buy 3.25 lb of tomatoes. If Jamal only
has $10, from which store(s) could he purchase his
tomatoes? Check all that apply.
Store A
Store B
Store C
Store D
Store E
A
$3.10 per pound
B
$3.02 per pound
с
$2.97 per pound
D
$3.07 per pound
E
$3.09 per pound

I thought of a two-digit number. The unit digit of my number is 7 more than the tens digit cubed. What is my number?

If b^2 = 25 then b= Answer it please

Xis normally distributed with mean 1,000 and standard deviation 250. What is the probability that X lies between 800 and 1, 100?

I need help the instructions say go left to right

A gallon of gas costs an average of two dollars is Betty spends $144 a month on gas determine how many gallons of gas she uses a month

your job requires that you work at least 40 hours a week you have already worked 15 and there are 4 more days left in the week how many hours do you have to work each day to get at least 40 hours: inequality and solution

the first number in the pattern is 32 the rule is to add 27​

anyone in flvs? we should find each other in live lessons lol

If a roof has a pitch of 5 to 11, how high will the roof rise over a 33-foot run?
a.
3
C.
2
72 feet
1 feet
b. 15 feet
d.
20 feet

8 tomatoes for $2 unit rate
I don't have much so please 17

estimate the answer for 1 2/3 x 5 1/10 (type a whole number​

Michael exercises more than 35 minutes per day.
Use t to represent Michael's amount of exercise (in minutes per day).

natalie budgets $150 for yoga training but doesn’t want to spend all of that money. She buys a yoga mat for $10 and spends $9 per day on yoga classes. Which inequality represents the number of day,d, that Natalie can take classes and stay under (less than) her budget?

find the sum of 2x ÷ x-1 and x÷x-1​

You have 8 donuts and you want to give 1/4 of them to a friend. How many donuts would your friend get?​

A newspaper is launching a new advertising campaign in order to increase the number of daily subscribers. The newspaper currently ​(t​0) has​ 26,000 daily subscribers and management expects that​ number, S(t), to grow at the rate of subscribers per​ day, where t is the number of days since the campaign began. How long​ (to the nearest​ day) should the campaign last if the newspaper wants the number of daily subscribers to grow to​ 49,000?

Write an equation in the line in slope intercept form

7th grade math help me plzzzz

QUICK
solve this equation
a^n+b^n=

A square patio has an area of 135 square feet. How long is each side of the patio to the nearest tenth?
Each side of the patio is approximately
feet long.

Its late and i need this pls









Gretchen made a paper cone to hold a gift for a friend. The paper cone was 11 inches high and had a radius of 4 inches. Find the volume of the paper cone to the nearest tenth. Use 3.14 for π.


The volume is ___in^3

Toby works at an amusement park. He loads 10 new passengers onto the roller coaster every
3/4
of a minute. At what rate does Toby load passengers?

Pleaseeee

Question:
7x^2 + 8x = x^2