Mathematics, 01.07.2020 15:01 Lydiaxqueen

Suppose a simple random sample of size n = 1000 is obtained from a population whose size i: N = 2,000,000 and whose population proportion with a specified characteristic is p = 0.76. Complete parts (a) through (c) below. 1. What is the probability of obtaining x = 790 or more individuals with the characteristic?
2. What is the probability of obtaining x =740 or fewer individuals with the characteristic?

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Answer from: sonnie28

1. 1.46% probability of obtaining x = 790 or more individuals with the characteristic

2. 7.49% probability of obtaining x =740 or fewer individuals with the characteristic

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 = 1000, p = 0.76

$\mu = E(X) = np = 1000*0.76 = 760$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1000*0.76*0.24} = 13.51$

1. What is the probability of obtaining x = 790 or more individuals with the characteristic?

Using continuity correction, this is $P(X \geq 790 - 0.5) = P(X \geq 789.5)$ , which is 1 subtracted by the pvalue of Z when X = 789.5. So

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

$Z = \frac{789.5 - 760}{13.51}$

Z = 2.18

Z = 2.18 has a pvalue of 0.9854

1 - 0.9854 = 0.0146

1.46% probability of obtaining x = 790 or more individuals with the characteristic.

2. What is the probability of obtaining x =740 or fewer individuals with the characteristic?

Using continuity correction, this is $P(X \leq 740 + 0.5) = P(X \leq 740.5)$ , which is the pvalue of Z when X = 740.5. So

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

$Z = \frac{740.5 - 760}{13.51}$

Z = -1.44

Z = -1.44 has a pvalue of 0.0749

7.49% probability of obtaining x =740 or fewer individuals with the characteristic

Answer from: Quest

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.