Mathematics, 16.07.2021 01:50, pookie879

Consider the probability that more than 97 out of 120 people will get the flu this winter. Assume the probability that a given person will get the flu this winter is 97%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

Answers: 1

Show answers

Answers

Since n(1-p) = 3.6 < 5 , the normal distribution cannot be used as an approximation to the binomial probability to approximate the probability.

Using the binomial distribution, 100% probability that more than 97 out of 120 people will get the flu this winter.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

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

Assume the probability that a given person will get the flu this winter is 97%.

This means that p = 0.97

120 people

This means that n = 120

Verifying the necessary conditions.

np = 120*0.97 = 116.4

n(1-p) = 120*0.03 = 3.6

Since n(1-p) = 3.6 < 5 , the normal distribution cannot be used as an approximation to the binomial probability to approximate the probability. Thus, the binomial distribution has to be used.

Probability using the binomial distribution:

P(X 97) = P(X = 98) + ... + P(X = 120)

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 98) = C_{120,98}.(0.97)^{98}.(0.03)^{22} \approx 0$

Probability close to 0, but below the mean, which means that the probability of the number being above this is 100%.

Using the binomial distribution, 100% probability that more than 97 out of 120 people will get the flu this winter.

answered: Guest

820,000 is the answr

answered: Guest

unless if u could do my questions, if not i wouldn't want to

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 21:10, madisontrosclair2

Plot a point at the y-intercept of the following function on the provided graph. 3y=-5x+7 20 points

Answers: 1

continue

Mathematics, 21.06.2019 21:30, Reebear1447

Abicycle training wheel has a radius of 3 inches. the bicycle wheel has a radius of 10 inches. approximately how much smaller, in square inches and rounded to the nearest hundredth, is the area of the training wheel than the area of the regular wheel? *

Answers: 3

continue

Mathematics, 21.06.2019 22:00, hannahpalmario

The customer price index(cpi), which measures the cost of a typical package of customer goods, was 208.8 in 2011 and 244.1 in 2016.let x=11 corresponding to the year 2011 an estimate to cpi into 2013 and 2014. assume that the data can be modeled by a straight line and the trend to continue idenfinitely. use data points to find such a line and then estimate the requested quantities

Answers: 1

continue

Mathematics, 22.06.2019 00:00, cutie22327

This summer the number of tourists in salem increased 4.5% from last years total of 426000. how many more tourists came to salem this summer

Answers: 1

continue

Do you know the correct answer?

Consider the probability that more than 97 out of 120 people will get the flu this winter. Assume th...