Round 4,938,503 to the nearest 100

An individual repeatedly attempts to pass a driving test. Suppose that the probability of passing the test with each attempt is

vladimir1956 [14]

Answer:

a) Our random variable X="number of tests taken until the individual passes" follows a geomteric distribution with probability of success p=0.25

For this case the probability mass function would be given by:

$P(X= k) = (1-p)^{k-1} p , k = 1,2,3,...$

b) $P(X \leq 3) = P(X=1) +P(X=2) +P(X=3)$

$P(X= 1) = (1-0.25)^{1-1} *0.25 = 0.25$

$P(X= 2) = (1-0.25)^{2-1} *0.25 = 0.1875$

$P(X= 3) = (1-0.25)^{3-1} *0.25 = 0.1406$

And adding the values we got:

$P(X \leq 3) =0.25+0.1875+0.1406=0.578$

c) $P(X \geq 5) = 1-P(X$

And we can find the individual probabilities:

$P(X= 1) = (1-0.25)^{1-1} *0.25 = 0.25$

$P(X= 2) = (1-0.25)^{2-1} *0.25 = 0.1875$

$P(X= 3) = (1-0.25)^{3-1} *0.25 = 0.1406$

$P(X= 4) = (1-0.25)^{4-1} *0.25 = 0.1055$

$P(X \geq 5) = 1-[0.25+0.1875+0.1406+0.1055]= 0.316$

Step-by-step explanation:

Previous concepts

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

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

Let X the random variable that measures the number of trials until the first success, we know that X follows this distribution:

$X\sim Geo (1-p)$

Part a

Our random variable X="number of tests taken until the individual passes" follows a geomteric distribution with probability of success p=0.25

For this case the probability mass function would be given by:

$P(X= k) = (1-p)^{k-1} p , k = 1,2,3,...$

Part b

We want this probability:

$P(X \leq 3) = P(X=1) +P(X=2) +P(X=3)$

We find the individual probabilities like this:

$P(X= 1) = (1-0.25)^{1-1} *0.25 = 0.25$

$P(X= 2) = (1-0.25)^{2-1} *0.25 = 0.1875$

$P(X= 3) = (1-0.25)^{3-1} *0.25 = 0.1406$

And adding the values we got:

$P(X \leq 3) =0.25+0.1875+0.1406=0.578$

Part c

For this case we want this probability:

$P(X \geq 5)$

And we can use the complement rule like this:

$P(X \geq 5) = 1-P(X$

And we can find the individual probabilities:

$P(X= 1) = (1-0.25)^{1-1} *0.25 = 0.25$

$P(X= 2) = (1-0.25)^{2-1} *0.25 = 0.1875$

$P(X= 3) = (1-0.25)^{3-1} *0.25 = 0.1406$

$P(X= 4) = (1-0.25)^{4-1} *0.25 = 0.1055$

$P(X \geq 5) = 1-[0.25+0.1875+0.1406+0.1055]= 0.316$

3 0

3 years ago

What was the cause of the revolutionary war? Comment

VikaD [51]

Answer:by colonial opposition to British attempts to impose greater control over the colonies and to make them repay the crown for its defense of them during the French and Indian War (1754–63)

5 0

3 years ago

Ashley deposits $10 000 at the end of each month for 6 times at rate of 5% compounded monthly. How much will be in her account

xz_007 [3.2K]

The future values of Ashley's periodic deposits under the five scenarios are stated in the deposit table as follows:

<h3>Deposit Table:</h3>

Item Initial Periodic Deposit Interest Future Value Interest

Deposit Deposit Period Rate ($)

a. $10,000 $10,000 6 months 5% $61,774.51 $1,774.51

b. $10,000 $10,000 3 months 5% $30,502.78 $502.78

c. $10,000 $10,000 6 months 5% $51,774.51 $1,522.42

d. $20,000 $10,000 6 months 5% $72,201.71 $2,201.71

e. $10,000 $10,000 6 months 5%/6% $60,803.78 $803.78

<h3>What is the future value?</h3>

The future value of a periodic investment represents the present value of cash flows compounded at an interest rate into the future.

The future value is computed using the FV formula or factor.

It can also be computed using an online finance calculator as follows:

<h3>Data and Calculations:</h3>

Periodic Deposit = $10,000

Investment period = 6 months

Interest rate = 5% compounded monthly

<h3>a) for illustration:</h3>

N (# of periods) = 6 months

I/Y (Interest per year) = 5%

PV (Present Value) = $0

PMT (Periodic Payment) = $10,000

<u>Results</u>:

FV = $61,774.51

Sum of all periodic payments = $60,000 ($10,000 x 6)

Total Interest = $1,774.51

<h3>Other Special Cases:</h3>

c) Interest on $10,000 for 3 months is $1,522.42 ($1,774.51 - $252.09).

d) Future Value Interest

5% with $20,000 $82,285.04 $2,285.04

5% with $10,000 (10,083.33) (83.33)

Total for 6 months $72,201.71 $2,201.71

e) Future Value Interest

5% for 3 months $30,502.78 $502.78

6% for 3 months $30,301.00 $301.00

Total for 6 months $60,803.78 $803.78

Learn more about the computation of future values at brainly.com/question/24703884 and brainly.com/question/12979998

#SPJ1

4 0

2 years ago

How many m are in 300 mm

Ksivusya [100]

There are 1,000 mm in a m. So with that said you would do 300/1000. This equals 0.3.
So your answer is going to be 0.3
Hope this helps :)

5 0

3 years ago

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Please help quickly !!!! thank youuu!

Alecsey [184]

Answer: you multiply the 2 numbers and divide it by half then your answer is the easy way to do it.

Step-by-step explanation:

8 0

2 years ago

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