What are the answers for a and B ?

Suppose that 16% of the population of the U.S. is left-handed. If a random sample of 170 people from the U.S. is chosen, approxi

Shalnov [3]

Answer:

0.6064 = 60.64% probability that fewer than 29 are left-handed.

Step-by-step explanation:

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 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

16% of the population of the U.S. is left-handed.

This means that $p = 0.16$

Sample of 170 people

This means that $n = 170$

Mean and standard deviation:

$\mu = E(X) = np = 170*0.16 = 27.2$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{170*0.16*0.84} = 4.78$

Probability that fewer than 29 are left-handed.

Using continuity correction, this is P(X < 29 - 0.5) = P(X < 28.5), which is the pvalue of Z when X = 28.5. So

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

$Z = \frac{28.5 - 27.2}{4.78}$

$Z = 0.27$

$Z = 0.27$ has a pvalue of 0.6064

0.6064 = 60.64% probability that fewer than 29 are left-handed.

6 0

3 years ago

if two angles of a triangle are complementary find the number of degrees in the third angle of the triangle

Norma-Jean [14]

Answer:

The measure of the third angle is a 90 degrees

Step-by-step explanation:

Let

A and B ----> two complementary angles in a triangle

C ---> the measure of the third angle in a triangle

we know that

If two angles are complementary, then their sum is equal to 90 degrees

so

$A+B=90^o$ ---> equation A

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

$A+B+C=180^o$ ----> equation B

substitute equation A in equation B

$(90^o)+C=180^o$

solve for C

subtract 90 degrees both sides

$C=180^o-90^o$

$C=90^o$

therefore

we have a right triangle

7 0

4 years ago

Please help I need the answer by 23rd (5 points).

IrinaK [193]

Answer:

The relationship between the lengths of the sides of the triangle is that they all follow the Pythagorean Theorem (at least I'm pretty sure that's the answer.

Step-by-step explanation:

If you plug in the smaller sides like 9^2+40^2 which equals to 1681. Then you square 1681, you'll get 41 as your hypotenuse. The sides of triangle provided above your question, should follow the formula given to you which is c^2=a^2+b^2. Just to be safe, you can check if all of the triangle sides actually are true for the Pythagorean theorem.

3 0

3 years ago

What is the product of (2x2 + 4x-2) and 3x+6)?

Setler79 [48]

Answer:

${24x}^{2} + 42x - 12$