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

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation:

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: