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?

Answers: 3

Show answers

Answers

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

step-by-step explanation:

Answer from: Quest

The answer is: y would equal 3 because if you simplify the equation then it would be y= 3x+9 and if you divide 3x and 9 by 3 it would equal 3. y= 3

Another question on Mathematics

Mathematics, 21.06.2019 16:00

Data are collected to see how many ice-cream cones are sold at a ballpark in a week. day 1 is sunday and day 7 is the following saturday. use the data from the table to create a scatter plot.

Answers: 2

Answer

Mathematics, 21.06.2019 21:30

Aye asap pls ! markin da brainiest too ! btw da step choices are all add, distribute, divide, n subtract

Answers: 2

Answer

Mathematics, 22.06.2019 00:30

The mean average cost of standard room per night at a hostel is ? 20.60. therefore, how much does a standard room cost per night at night-time rest days?

Answers: 1

Answer

Mathematics, 22.06.2019 01:30

Add: (6x^2-5x+3) + (3x^3+7x-8) a. 9x^2+12x-5 b. 9x^2+2x+11 c. 9x^2+2x-5 d. 9x^2-2x+5

Answers: 1

Answer

You know the right answer?

Suppose a simple random sample of size n = 1000 is obtained from a population whose size i: N = 2,00...

Questions