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Rudik [331]
3 years ago
12

​In a sample of 800 U.S.​ adults, 199 think that most celebrities are good role models. Two Two U.S. adults are selected at rand

om from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.​adults, complete parts​ (a) through​ (c).
(a) Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is ________?(Round to three decimal places as​ needed.)

​(b) Find the probability that neither adult thinks most celebrities are good role models. The probability that neither adult thinks most celebrities are good role models is _______?(Round to three decimal places as​ needed.) ​

(c) Find the probability that at least one of the two adults thinks most celebrities are good role models. The probability that at least one of the two adults thinks most celebrities are good role models ______? (Round to three decimal places as​ needed.)

Expert Answer
Mathematics
1 answer:
mel-nik [20]3 years ago
6 0

Answer:

Step-by-step explanation:

Given that in a sample of 800 U.S.​ adults, 199 think that most celebrities are good role models. Two Two U.S. adults are selected at random from the population of all U.S. adults without replacement.

In 800 adults 199 are favourable and remaining 601 are against.

a) The probability that both adults think most celebrities are good role models is ________= Prob of selecting both from 199

= \frac{199C2}{800C2} \\=0.0616

=0.062

b) The probability that neither adult thinks most celebrities are good role models is _______=P(both selecting from 601)

=  \frac{601C2}{800C2} \\=0.5641

=0.564

c) The probability that at least one of the two adults thinks most celebrities are good role models ______

=1-Prob that neither thinks

= 1- 0.564

= 0.436

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Nevaeh invested $660 in an account paying an interest rate of 3% compounded
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Answer:

19

Step-by-step explanation:

Rate 1: 3  

4

1

​  

%=3+1/4=

\,\,3.25\%\rightarrow 0.0325

3.25%→0.0325

\text{Rate 2: }3\tfrac{1}{8}\%=3+1/8=

Rate 2: 3  

8

1

​  

%=3+1/8=

\,\,3.125\%\rightarrow 0.03125

3.125%→0.03125

\text{Calculate Final Amount for Nevaeh}

Calculate Final Amount for Nevaeh

\overline{\phantom{\text{Calculate Final Amount for Nevaeh}}}

Calculate Final Amount for Nevaeh

 

\text{Compounded Continuously:}

Compounded Continuously:

A=Pe^{rt}

A=Pe  

rt

 

P=660\hspace{35px}r=0.0325\hspace{35px}t=14

P=660r=0.0325t=14

Given values

A=660e^{0.0325(14)}

A=660e  

0.0325(14)

 

Plug in

A=660e^{0.455}

A=660e  

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Multiply

A=1040.2744

A=1040.2744

Use calculator (with e button)

\text{Calculate Final Amount for Jonathan}

Calculate Final Amount for Jonathan

\overline{\phantom{\text{Calculate Final Amount for Jonathan}}}

Calculate Final Amount for Jonathan

 

\text{Compounded Monthly:}

Compounded Monthly:

A=P\left(1+\frac{r}{n}\right)^{nt}

A=P(1+  

n

r

​  

)  

nt

 

Compound interest formula

P=660\hspace{35px}r=0.03125\hspace{35px}t=14\hspace{35px}n=12

P=660r=0.03125t=14n=12

Given values

A=660\left(1+\frac{0.03125}{12}\right)^{12(14)}

A=660(1+  

12

0.03125

​  

)  

12(14)

 

Plug in values

A=660(1.0026042)^{168}

A=660(1.0026042)  

168

 

Simplify

A=1021.6468

A=1021.6468

Use calculator

\text{How much more money Nevaeh has:}

How much more money Nevaeh has:

1040.2744-1021.6468

1040.2744−1021.6468

18.6276

18.6276

\$ 19

$19

4 0
3 years ago
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