Suppose that a random sample of eighteen recently sold houses in a certain city has a mean sales price of , with a standard deviation of . Under the assumption that house prices are normally distributed, find a confidence interval for the mean sales price of all houses in this community. Then find the lower limit and upper limit of the confidence interval.

This question is incomplete, the complete question is;

Suppose that a random sample of eighteen recently sold houses in a certain city has a mean sales price of $280,000, with a standard deviation of $10,000. Under the assumption that house prices are normally distributed, find a 95% confidence interval for the mean sales price of all houses in this community. Then find the lower limit and upper limit of the confidence interval.

At 95%, confidence interval is ( 275026.7, 284973.3 )

Hence;

Lower limit = 275026.7

Upper limit = 284973.3

Step-by-step explanation:

 Given that;

mean x = $280,000

standard deviation σ = $10,000

sample size n = 18

degree of freedom df = n - 1 = 18 - 1 = 17

∝ = 1 - 95% = 1 - 0.95 = 0.05  

so

Critical t value = tinv( 0.05, 17 ) = 2.11

now, at 95% confidence interval for mean will be;

⇒ x ± [ Critical t value × ( σ/√n) ]

so we substitute

⇒ 280,000 ± [  2.11 × ( 10000/√18) ]

⇒ 280,000 ± [  2.11 × 2357.0226 ]

⇒ 280,000 ± 4973.3

⇒ 280000 - 4973.3, 280000 + 4973.3

At 95%, confidence interval is ( 275026.7, 284973.3 )

Hence;

Lower limit = 275026.7

Upper limit = 284973.3

i did it myself and i got 4.2 (b) hope its right

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.