According to a research center, 16% of all merchandise sold in a particular country gets returned. A department store in a certain city sampled 80 items sold in January and found that 24 of the items were returned. (a) Construct a point estimate of the proportion of items returned for the population of sales transactions at the store in the given city. (b) Construct a 95% confidence interval for the proportion of returns at the store in the given city. (Round your answers to four decimal places.) to

a) point estimate of the proportion of items returned for the population of sales transactions at the store in the given city

Point estimate = 0.3

b) The 95% confidence interval for the proportion of returns at the store in the given city

( 0.19958,0.40042)

Step-by-step explanation:

Given the Population proportion 'P'= 16% = 0.16

Given data a department store in a certain city sampled 80 items sold in January and found that 24 of the items were returned

The sample proportion

here x =24 and n = 80

The sample proportion

a) Point estimate:-

A point estimate of the true proportion P

Point estimate =

point estimate of the proportion of items returned for the population of sales transactions at the store in the given city

b) The 95%  confidence interval for the proportion

The 95% confidence interval for the proportion of returns at the store in the given city

substitute all values we get ,

on simplification, we get

(0.3-0.10042 ,0.3+0.10042)

( 0.19958,0.40042)

Conclusion:-

a)  point estimate of the proportion of items returned for the population of sales transactions at the store in the given city

Point estimate = 0.3

b) The 95% confidence interval for the proportion of returns at the store in the given city

( 0.19958,0.40042)

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

its kind of blurry. can you put a clearer pic?

step-by-step explanation: