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.

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answered: 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

answered: Guest

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

$a_{n}=a+(n-1)d\\ =19-5(n-1)\\=24-5n$

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

answered: Guest

Sin(a)+cos(a)+cot(a)-1=2(csc(x)+1)

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