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3 years ago

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A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of w

hich is correct. Find the probability that the student gets exactly 15 correct answers. Use the normal distribution to aproximate the binomial distribution.
0.7967
0.0606
0.0823
0.8577

2 answers:

lubasha [3.4K]3 years ago

8 0

The best option is C. 0.0823mean = np = 48*1/4 = 12

SD = sqrt(npq) = sqrt(48 *1/4 *3/4) = 3

aplying continuity correction for using a continuous distribution for a discrete one,

"exactly 15" means 14.5 to 15.5

z1= (14.5-12)/3 = 0.833 , z2 = (15.5-12)/3 = 1.167

P(0.833 < z < 1.167) = 0.0808

andreyandreev [35.5K]3 years ago

7 0

Answer:

Correct answer is C

Step-by-step explanation:

First we need to find expected value of the event:

$E(x)=n*p=48*0.25=12$

And standard deviation of the event:

$Var(x)=\sqrt{n*p*q} =\sqrt{48*0.25*0.75} =3$

Then need to z value of normal distribution function for 15.5 and 14.5 correct answers:

$z_{1}=(15.5-12)/3=1.167\\z_{2}=(14.5-12)/3=0.833$

$P(z_{1})=0.8790\\P(z_{2})=0.7967$

P(15)=0.8790-0.7967=0.0823

Ps. Please find z table at the attachment.

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