Mathematics, 25.11.2020 14:00 AnaiyaKirksey8

The chances that a student will get 7 marks out of 10 in first attempt of a certain Quiz while attempting Quiz on BlackBoard LMS is 40%. Suppose that 20 students are selected at random then find a probability that i)Exactly 12 students will get 7 marks out 10 in the Quiz. ii)Fewer than 10 students will get 7 marks out 10 in the Quiz. iii)At least 5 students will get 7 marks out 10 in the Quiz.

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Answer from: sheram2010

i) P(X=12)=0.0355

ii) P(X

iii) $P(X\geq 5)=0.9490$

Step-by-step explanation:

Let's start by defining the random variable ⇒

'' Number of students that will get 7 marks out of 10 in first attempt of a certain Quiz while attempting Quiz on BlackBoard LMS ''

is a discrete random variable.

The probability of a randomly selected student getting 7 marks out of 10 is 0.4

(This is a data from the question).

Now, if we assume independence between the students while they are doing the Quiz and also we assume that this probability remains constant , we can modelate as a binomial random variable ⇒

~ Bi (n,p)

Where ''n'' and ''p'' are the parameters of the variable.

''n'' is the number of students attempting the Quiz and ''p'' is the probability that a student will get 7 marks out of 10 which is 0.4 ⇒

~ Bi (20, 0.4) in the question.

The probability function for is

$p_{X}(x)=P(X=x)=\left(\begin{array}{c}n&x\end{array}\right)p^{x}(1-p)^{n-x}$ (I)

Where $\left(\begin{array}{c}n&x\end{array}\right)$ is the combinatorial number define as

$\left(\begin{array}{c}n&x\end{array}\right)=\frac{n!}{x!(n-x)!}$

Replacing the parameters in the equation (I) ⇒

$P(X=x)=\left(\begin{array}{c}20&x\end{array}\right)(0.4)^{x}(0.6)^{20-x}$ (II)

For i) we need to find P(X=12)

Then, we only need to replace by x=12 in equation (II) ⇒

$P(X=12)=\left(\begin{array}{c}20&12\end{array}\right)(0.4)^{12}(0.6)^{8}=0.0355$

For ii) we need to calculate P(X

This probability is equal to ⇒ P(X and to calculate it we need to sum P(X=0)+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)

We can do it summing each term or either using any program.

The result is P(X

Finally for iii) we need to find ⇒ $P(X\geq 5)$

This probability is equal to ⇒ $P(X\geq 5)=1-P(X\leq 4)$ ⇒

$1-P(X\leq 4)=1-[P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)]$

Again we can find each term by using the equation (II) or either using a program. The result is $P(X\geq 5)=0.9490$

Answer from: Quest

step-by-step explanation:

Answer from: Quest

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

$\text{simple interest} = \frac{principal\times rate\times time}{100} \\\\\text{simple interest} = \frac{1000\times 4\times 10}{100}=\$400\\\\amount = principal + interest\\amount = 1000 + 400 = \$1400$

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

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