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3 years ago

Simplifying square root

Mathematics

2 answers:

Solnce55 [7]3 years ago

4 0

It should be A, 6! I hope all is well and you pass!

oee [108]3 years ago

3 0

Answer is A. 6
hope it helps

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A boy's mother was 32 years old when he was born. Let a represent the boy's age and m represent the mother's age.

LenKa [72]

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2 years ago

Find the midpoint of the line segment joining the points (−1,−2) and (−3,9).

FromTheMoon [43]

Answer:

Step-by-step explanation:

Midpoint = (x₁+ x₂)/2 , (y₁ +y₂)/2

= [(-1)+(-3))/2] , (-2 + 9)/2

= (-4/2) , (-7/2)

= (-2 , -3.5)

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3 years ago

A surgical technique is performed on eleven patients. You are told there is 90% chance of success. Find the probability that the

Alexandra [31]

Answer:

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Step-by-step explanation:

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3 0

3 years ago

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

Pepsi [2]

Answer:

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

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

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