¿Cual es la medida del diámetro del circulo unitario?

Suppose that scores on a test are normally distributed with a mean of 80 and a standard deviation of 8. Which of the following q

Ilia_Sergeevich [38]

Answer:

a) 86.73

b) 90.24

c) 10.56% scoring more than 90

d) 75.8

e) 50% probability that a randomly selected student will score more than 80.

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 80, \sigma = 8$

a. Find the 80th percentile.

This is the value of X when Z has a pvalue of 0.8. So X when Z = 0.841.

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

$0.841 = \frac{X - 80}{8}$

$X - 80 = 8*0.841$

$X = 86.73$

b. Find the cutoff for the A grade if the top 10% get an A.

This is the value of X when Z has a pvalue of 0.9. So X when Z = 1.28.

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

$1.28 = \frac{X - 80}{8}$

$X - 80 = 8*1.28$

$X = 90.24$

c. Find the percentage scoring more than 90.

This is 1 subtracted by the pvalue of Z when X = 90. So

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

$Z = \frac{90 - 80}{8}$

$Z = 1.25$

$Z = 1.25$ has a pvalue of 0.8944.

1 - 0.8944 = 0.1056

10.56% scoring more than 90

d. Find the score that separates the bottom 30% from the top 70%.

This is the value of X when Z has a pvalue of 0.3. So X when Z = -0.525.

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

$-0.525 = \frac{X - 80}{8}$

$X - 80 = 8*(-0.525)$

$X = 75.8$

e. Find the probability that a randomly selected student will score more than 80.

This is 1 subtracted by the pvalue of Z when X = 80.

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

$Z = \frac{80 - 80}{8}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5.

1 - 0.5 = 0.5

50% probability that a randomly selected student will score more than 80.

8 0

3 years ago

How do you Simplify the expression completely.<br><br> c(4b3+3a)+b(2cb2−6ac) <br> Click

Dafna1 [17]

Answer:

c×3 (2 b^3 - 2 a b + a)

Step-by-step explanation:

Simplify the following:

c (4 b^3 + 3 a) + b (2 c b^2 - 6 a c)

Hint: | Factor common terms out of 2 c b^2 - 6 a c.

Factor 2 c out of 2 c b^2 - 6 a c:

c (4 b^3 + 3 a) + b×2 c (b^2 - 3 a)

Hint: | Pull a common factor out of c (4 b^3 + 3 a) + b×2 c (b^2 - 3 a).

Factor c out of c (4 b^3 + 3 a) + b×2 c (b^2 - 3 a), resulting in c ((4 b^3 + 3 a) + b×2 (b^2 - 3 a)):

c (4 b^3 + 3 a + 2 b (b^2 - 3 a))

Hint: | Distribute 2 b over b^2 - 3 a.

2 b (b^2 - 3 a) = 2 b^3 - 6 a b:

c (4 b^3 + 3 a + 2 b^3 - 6 a b)

Hint: | Group like terms in 4 b^3 + 3 a - 6 a b + 2 b^3.

Grouping like terms, 4 b^3 + 3 a - 6 a b + 2 b^3 = (4 b^3 + 2 b^3) - 6 a b + 3 a:

c (4 b^3 + 2 b^3) - 6 a b + 3 a

Hint: | Add like terms in 4 b^3 + 2 b^3.

4 b^3 + 2 b^3 = 6 b^3:

c (6 b^3 - 6 a b + 3 a)

Hint: | Factor out the greatest common divisor of the coefficients of 6 b^3 - 6 a b + 3 a.

Factor 3 out of 6 b^3 - 6 a b + 3 a:

Answer: c×3 (2 b^3 - 2 a b + a)

7 0

3 years ago

A chocolate chip cookie recipe needs 2 cups of chocolate chips and teaspoon of salt. If the recipe is increased to 6 cups of cho

olasank [31]

Answer:

3 teaspoons

Step-by-step explanation:

Since we need 1 teaspoon for 2 cups, I would only assume we would keep adding a teaspoon for every 2 additional cups of chocolate chips.

2 + 2 + 2 = 6

We would need an additional teaspoon of salt for each of the sets of two.

5 0

3 years ago

Simplify each expression.

Elina [12.6K]

Step-by-step explanation:

remember that x^-n means 1/(x^n).

x^a × x^b = x^(a+b)

x^a / x^b = x^(a-b)

(x^a)^b = x^(a×b)

(x×y)^n = x^n × y^n

so,

a^2 / a^-2 = a^(2 - -2) = a^4

and

b^-3 / b^2 = b^(-3 - 2) = b^-5 = 1/(b^5)

that means we have then :

(a^4 × b^-5)^2 = (a^4)^2 × (b^-5)^2 = a^8 × b^-10 =

= a^8 / b^10 = a⁸/b¹⁰

5 0

3 years ago

Please help me with this question please help

a_sh-v [17]

Answer: A) 24.8 B) 8.8

Step-by-step explanation:

You could try using cosine ( adj. over hypotenuse) on a calculator.

6 0

3 years ago

¿Cual es la medida del diámetro del circulo unitario? ​

¿Cual es la medida del diámetro del circulo unitario?