Answer to Question #175490 in Statistics and Probability for Denisse Bisuña

Question

1.Given X and n, find p and q. Show your calculation steps.

a. X = 28; n = 100

b. X = 45; n = 240

c. X = 120; n = 1000

d. X = 234; n = 1500

e. X = 318; n = 2300

2.Estimate the population proportions for each of the following data:

a. In a plant box consisting of 120 seedlings, 80 seedlings were treated with growth enhancer. Estimate p and q, where p is the proportion of seedlings with growth enhancer.

b. In a survey of 80 children, 48 like to watch horror films. Find p and q, where p is the proportion of children who like to watch horror films.

3.In a political rally, an opinion poll was conducted among the present voters whether they agree with the platform of the candidate. Two hundred and one (201) said they agree. If there were 500 individuals in the sample, what is p? What is q?

Answer 1

1.

a. $\bar{x}=np, q=1-p$

$$p=\dfrac{\bar{x}}{n}=\dfrac{28}{100}=0.28$$

$$q=1-p=1-0.28=0.72$$

b. $\bar{x}=np, q=1-p$

$$p=\dfrac{\bar{x}}{n}=\dfrac{45}{240}=0.1875$$

$$q=1-p=1-0.1875=0.8125$$

c. $\bar{x}=np, q=1-p$

$$p=\dfrac{\bar{x}}{n}=\dfrac{120}{1000}=0.12$$

$$q=1-p=1-0.12=0.88$$

d. $\bar{x}=np, q=1-p$

$$p=\dfrac{\bar{x}}{n}=\dfrac{234}{1500}=0.156$$

$$q=1-p=1-0.156=0.844$$

e. $\bar{x}=np, q=1-p$

$$p=\dfrac{\bar{x}}{n}=\dfrac{318}{2300}=\dfrac{159}{1150}$$

$$q=1-p=1-\dfrac{159}{1150}=\dfrac{991}{1150}$$

2.

a.

$$p=\dfrac{x}{n}=\dfrac{80}{120}=\dfrac{2}{3}$$

$$q=1-p=1-\dfrac{2}{3}=\dfrac{1}{3}$$

b.

$$p=\dfrac{x}{n}=\dfrac{48}{80}=0.6$$

$$q=1-p=1-0.6=0.4$$

3.

Suppose each present voter agrees or does not agree with the platform of the candidate. Then $p$ is the proportion of voters who agrees with the platform of the candidate. 

$$p=\dfrac{x}{n}=\dfrac{201}{500}=0.402$$

 $q$  is the proportion of voters who does not agree with the platform of the candidate. 

$$q=1-p=1-0.402=0.598$$