A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses, Estimate the probability of getting at least 12 correct answers. (Hint: Use the Normal Approximation to binomial).

0.8508

Step-by-step explanation:

In this question, we are asked to estimate the probability of getting at least 12 correct answers.

X ~ Bin ( n , p)

Where n = 60 , p = 1/4 = 0.25

Mean = np = 60 * 0.25 = 15

Standard deviation = sqrt [ n p ( 1 - p) ] = Sqrt [ 60 * 0.25 ( 1 - 0.25) ] = 3.3541

Using normal approximation

P(X < x) = P(Z < ( x - mean) / SD )

P(X >= 12) = P(X > 11.5)

= P(Z > ( 11.5 - 15) / 3.3541 )

= P(Z > -1.04)

= P(Z < 1.04)

= 0.8508

step-by-step explanation:

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)