The variable that says the number of correct questions follows a Binomial distribution, because there are n identical and independent events with a probability p of success and a probability 1-p of fail. So, the probability of get x questions correct is:

$P(x)=\frac{n!}{x!(n-x)!} *p^{x} *(1-p)^{n-x}$

Where n is equal to 10 questions and p is the probability of get a correct answers, so p is equal to 1/2

Then, if the student pass the test with at least 8 questions correct, the probability P of that is:

P = P(8) + P(9) + P(10)

$P=(\frac{10!}{8!(10-8)!}*0.5^{8}*(0.5)^{10-8})+(\frac{10!}{9!(10-9)!} *0.5^{9} *(0.5)^{10-9})+(\frac{10!}{10!(10-10)!} *0.5^{10} *(0.5)^{10-10})$

P = 0.0439 + 0.0097 + 0.0009

P = 0.0545

8 0

3 years ago

The dimensions of an iPhone are x – 2 and x + 3. If the area of an iPhone is 14 square inches, find the dimensions of the iPhone

QveST [7]

Answer:

The dimensions of the iphone are 2 inches by 7 inches.

Step-by-step explanation:

Given that,

The dimensions of an iPhone are x – 2 and x + 3.

The area of an iphone is 14 sq inches

We need to find the dimensions of the iPhone. It is in the shape of a rectangle. Its area is given by :

$A=l\times b\\\\(x-2)(x+3)=14\\\\x^2-2x+3x-6=14\\\\x^2+x-6-14=0\\\\x^2+x-20=0\\\\x^2+5x-4x-20=0\\\\x(x+5)-4(x+5)=0\\\\(x-4)(x+5)=0\\\\x=4\ and\ x=-5$

Neglecting negative value

First dimension = (x-2) = (4-2) = 2 inches

Other dimension = (x+3) = (4+3) = 7 inches

Hence, the dimensions of the iphone are 2 inches by 7 inches.

3 0

3 years ago