Mathematics, 31.03.2020 00:47, Wxaieyu

Consider the probability that no less than 96 out of 145 people will not get the flu this winter. Assume the probability that a given person will not get the flu this winter is 61%. Approximate the probability using the normal distribution. Round your answer to four decimal places.

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answered: nora45102p45bzz

0.1324 = 13.24% probability that no less than 96 out of 145 people will not get the flu this winter.

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 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 = 145, p = 0.61

$\mu = E(X) = np = 145*0.61 = 88.45$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{145*0.61*0.39} = 5.87$

Consider the probability that no less than 96 out of 145 people will not get the flu this winter.

More than 95 people, which is the same as 1 subtracted by the pvalue of Z when X = 95. So

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

$Z = \frac{95 - 88.45}{5.87}$

Z = 1.115

Z = 1.115 has a pvalue of 0.8676

1 - 0.8676 = 0.1324

0.1324 = 13.24% probability that no less than 96 out of 145 people will not get the flu this winter.

answered: Guest

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

$m\angle qrt=156^o$

$m\angle qst=156^o$

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

answered: Guest

31/6= 19/6 19/6 *1/7=19/42

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Consider the probability that no less than 96 out of 145 people will not get the flu this winter. As...