Mathematics, 16.07.2021 05:30 cynone8254

Consider the probability that exactly 90 out of 148 students will pass their college placement exams. Assume the probability that a given student will pass their college placement exam is 64%. Approximate the probability using the normal distribution. Round your answer to four decimal places.

Answers: 2

Show answers

Answers

Answer from: iikatreii

0.0491 = 4.91% probability that exactly 90 out of 148 students will pass their college placement exams.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

Assume the probability that a given student will pass their college placement exam is 64%.

This means that p = 0.64

Sample of 148 students:

This means that n = 148

Mean and standard deviation:

$\mu = E(X) = np = 148(0.64) = 94.72$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{148*0.64*0.36} = 5.84$

Consider the probability that exactly 90 out of 148 students will pass their college placement exams.

Due to continuity correction, 90 corresponds to values between 90 - 0.5 = 89.5 and 90 + 0.5 = 90.5, which means that this probability is the p-value of Z when X = 90.5 subtracted by the p-value of Z when X = 89.5.

X = 90.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{90.5 - 94.72}{5.84}$

Z = -0.72

Z = -0.72 has a p-value of 0.2358.

X = 89.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{89.5 - 94.72}{5.84}$

Z = -0.89

Z = -0.89 has a p-value of 0.1867.

0.2358 - 0.1867 = 0.0491.

0.0491 = 4.91% probability that exactly 90 out of 148 students will pass their college placement exams.

Answer from: Quest

The answer would be b

Answer from: Quest

step-by-step explanation:

the answer is a

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Solve this equation using substitution. {4x + y = −2} {4x + 6y = 44}

Answers: 1

Answer

Mathematics, 21.06.2019 19:20

When are triangles considered similar? a. corresponding angles are equal andcorresponding sides are proportionalb. corresponding angles are proportional andcorresponding sides are equalc. corresponding angles are equal orcorresponding sides are proportionald. corresponding angles are proportional orcorresponding sides are equal select the best answer from the choices providedmark this and retumsave and exitnext

Answers: 2

Answer

Mathematics, 21.06.2019 21:50

Which rule describes the composition of transformations that maps ajkl to aj"k"l"? ro. 900 o to, -2(x, y) to, -20 ro, 900(x, y) ro, 9000 t-2. o(x,y) t-2, 00 ro, 900(x, y)

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

What is perpendicular to y=-1/2x+11

Answers: 1

Answer

You know the right answer?

Consider the probability that exactly 90 out of 148 students will pass their college placement exams...

Questions