I need some help
A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets exactly 15 correct answers. Use the normal distribution to aproximate the binomial distribution.

I used BinomCdf(48,.25,15) and get 0.0767 but that isn't one of the choices. The choices are
0.7967
0.0606
0.0823
0.8577,

The best answer to this problem is 0.0823. np = 48 * 1/4 = 12 The exactly 15 would be written as 14.5 to 15.5. You then plug those into you equation separately. e1= (14.5-12)/3 = 0.833 and e2 =(15.5 - 12)/3 = 1.167) p(0.833<e<1.167)= 0.0808

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MrRoyal MrRoyal · Answer 2 · 2022-06-29T16:24:12+02:00

The probability that the student gets exactly 15 correct answers is 0.0823

How to determine the probability?

The given parameters are:

Sample size, n = 48
Correct answers, x = 15
Probability of right an answer, p = 0.25 i.e. 1 of 4 options is correct

Start by calculating the mean

[tex]\bar x = np[/tex]

[tex]\bar x = 48 * 0.25[/tex]

[tex]\bar x = 12[/tex]

Calculate the standard deviation

[tex]\sigma = \sqrt{np(1 -p)}[/tex]

[tex]\sigma = \sqrt{12 * (1 -0.25)}[/tex]

[tex]\sigma = 3[/tex]

To get exactly 15,we make use of the range 14.5 to 15.5.

So, we calculate the z scores at these values using:

[tex]z = \frac{x - \bar x}{\sigma}[/tex]

This gives

[tex]z = \frac{14.5 - 12}{3} = 0.83[/tex]

[tex]z = \frac{15.5 - 12}{3} = 1.17[/tex]

The probability is then calculated using

P(14.5 < x < 15.5) = p(0.83 < z < 1.17)

This gives

P(14.5 < x < 15.5) = 0.082269

Approximate

P(14.5 < x < 15.5) = 0.0823

Hence, the probability that the student gets exactly 15 correct answers is 0.0823

Read more about normal distribution at:

https://brainly.com/question/4079902

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