Mathematics, 23.03.2020 16:47 ciarapacheco

A certain question on a test is answered correctly by 22% of the respondents. Estimate the probability that among the next 150 responses there will be at most 40 correct answers.

Answers: 1

Show answers

Answers

Answer from: crawford184232323234

91.62% probability that among the next 150 responses there will be at most 40 correct answers

Step-by-step explanation:

I am going to use the binomial approximation 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 = 150, p = 0.22

$\mu = E(X) = np = 150*0.22 = 33$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150*0.22*0.78} = 5.07$

Estimate the probability that among the next 150 responses there will be at most 40 correct answers.

This is the pvalue of Z when X = 40. So

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

$Z = \frac{40 - 33}{5.07}$

Z = 1.38

Z = 1.38 has a pvalue of 0.9162

91.62% probability that among the next 150 responses there will be at most 40 correct answers

Answer from: Quest

idk sry

step-by-step explanation:

Answer from: Quest

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

$f(x) =\sqrt{x}$

this can also be written as

$y^{2} =x$

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.

Another question on Mathematics

Mathematics, 21.06.2019 15:30

The area of a rectangle is 15+5y square feet. which of the following expressions could be the length of the sides of the rectangle, in feet a. 5 and 3y b. 5 and 3+y c. 5 and 5+y d. 3 and 5+3y

Answers: 1

Answer

Mathematics, 21.06.2019 18:50

Expresa commuter train leaves downtown sation and travels at a average speed of 55 miles per hour towards the north side sation, which is 50miles away. thirty minutes later, express commuter train #7 leaves north side and travels at a average speed of 35miles per hour towards downtown sation. at the moment the two trains pass each other, how far(in miles) is train #12 from the downtown sation and how long(in minutes) has the #12 train been traveling

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

Aladder that is 20ft long is leaning against the side of a building. if the angle formed between the ladder and the ground is 75 degrees how far is the bottom of the from the base of the building?

Answers: 1

Answer

Mathematics, 22.06.2019 04:00

The graph of the function f(x) = (x + 2)(x + 6) is shown below. which statement about the function is true? the function is positive for all real values of x where x > –4. the function is negative for all real values of x where –6 < x < –2. the function is positive for all real values of x where x < –6 or x > –3. the function is negative for all real values of x where x < –2.

Answers: 2

Answer

You know the right answer?

A certain question on a test is answered correctly by 22% of the respondents. Estimate the probabili...

Questions