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inysia [295]
3 years ago
8

At the beginning of this month, the balance of Vance's checking account was $697.96. So far this month, he has received a payche

ck via direct deposit of $962.88, been charged a monthly service fee from his bank of $25.00, used a debit card linked to his account to make a purchase of $83.12, written a check for $138.83 that has already been deposited, and deposited a check written to him for $71.17. What is the current balance of Vance's checking account?
Mathematics
2 answers:
laila [671]3 years ago
6 0
His total account will have 1485.06 in it after everything is said and done.
WINSTONCH [101]3 years ago
4 0

Answer:

The current balance of Vance's checking account is $1485.06.

Step-by-step explanation:

Vance's checking account balance was $697.96

He has received a paycheck via direct deposit of $962.88

After receiving a paycheck his new account balance will be :

$697.96+$962.88 = $1660.84

He has been charged a monthly service fee from his bank of $25.00

So, amount $25.00 will be deducted from his account . So, new balance will be : $1660.84 - $25.00 =  $1635.84.

Now, he made  a purchase of $83.12 using his debit card . So, deduction of this amount will be done from the account .

So, new balance will be : $1635.84-$83.12 = $1552.72

He written a check of amount $138.83 . so  deduction of this amount will be done from the account .

So, new balance will be :$1552.72-$138.83= $1413.89

Now, he deposited a check written to him .of amount $71.17. so, addition of this amount will be done .

So, the new balance will be $1413.89+$71.17=$1485.06.

Thus , The current balance of Vance's checking account is $1485.06.

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Answer:

P(X \geq 7) = P(X=7) +P(X=8)

And we can find the individual probabilities using the probability mass function

P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826  

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And replacing we got:

P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131

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 "number of automobiles with both headligths working", on this case we now that:  

X \sim Binom(n=8, p=0.9)  

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!}  

And for this case we want to find this probability:

P(X \geq 7) = P(X=7) +P(X=8)

And we can find the individual probabilities using the probability mass function

P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826  

P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305  

And replacing we got:

P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131

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