Mathematics, 15.04.2020 01:38 montgomeryaevans

Suppose that about 55% of the people who are murdered actually knew the person who committed the murder. Suppose that a detective file in Boston has 51 current unsolved murders. What is the probability that fewer than 21 victims did not know their murderer?

Answers: 2

Show answers

Answers

Answer from: Yumimiku6539

24.51% probability that fewer than 21 victims did not know their murderer

Step-by-step explanation:

I am going to approximate the binomial probability distribution to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses 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 samples 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

n = 51, p = 0.55

$\mu = E(X) = np = 51*0.55 = 28.05$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{51*0.55*0.45} = 3.55$

What is the probability that fewer than 21 victims did not know their murderer?

That is, more than 30 knew the murdered.

$P(X \geq 30 + 0.5) = P(X \geq 30.5)$ , which is 1 subtracted by the pvalue of Z when X = 30.5. So

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

$Z = \frac{30.5 - 28.05}{3.55}$

Z = 0.69

Z = 0.69 has a pvalue of 0.7549

1 - 0.7549 = 0.2451

24.51% probability that fewer than 21 victims did not know their murderer

Answer from: Quest

its a trick question

step-by-step explanation:

dogs love water, just turn on the hose and it will run in circles chasing the water all day : )

Answer from: Quest

m∠5 + m∠3 = m∠1 is true.

m∠5 + m∠6 = 180 is true

m∠2 +m∠3 = m∠6 is true

m∠2 +m∠3 +m∠5 = 180 is true

Another question on Mathematics

Mathematics, 21.06.2019 20:00

Credit card a offers an introductory apr of 3.4% for the first three months and standard apr of 15.7% thereafter,

Answers: 3

Answer

Mathematics, 21.06.2019 21:30

Two rectangular prisms have the same volume. the area of the base of the blue prism is 418 4 1 8 square units. the area of the base of the red prism is one-half that of the blue prism. which statement is true?

Answers: 3

Answer

Mathematics, 22.06.2019 00:00

Answer asap! show all work! find the number of complex roots, the possible number of real roots and the possible rational roots of the polynomial function. then, solve for all roots. x^3 + 2x^2 + 3x + 6 = 0

Answers: 1

Answer

Mathematics, 22.06.2019 00:00

Apolygon is shown on the graph: a polygon is shown on the coordinate plane. vertices are located at 3 comma 5, 1 comma 3, 1 comma 1, 2 comma 0, 4 comma 0, 5 comma 1, and 5 comma 3. what effect will a translation 3 units down and 2 units left have on the polygon? be sure to address how it could impact the angles, side lengths, and congruency between the original pre-image and the image. xd i need

Answers: 3

Answer

You know the right answer?

Suppose that about 55% of the people who are murdered actually knew the person who committed the mur...

Questions

Mathematics, 24.10.2019 03:00

Brenda made 18 cups of lemonade. if each serving is 3/4 cup, how many servings did she make?...