Question

How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution.

35	110	40	100	65	70	30	23	100	110
105	95	105	60	110	120	95	90	60	70

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean price x and sample standard deviation s. (Round your answers to two decimal places.)

x =	$
s =	$

(b) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean price μ of all summer sleeping bags. (Round your answers to two decimal places.)

lower limit	$
upper limit	$

Answer 1

Solution:- Given that samples :
35,110,40,100,65,70,30,23,100,110,105,95,105,60,110,120,95,90,60,70

(a) X = 79.65
  
mean = sum of terms/number of terms
= 1593/20
= 79.65

standard deviation : s = 30.35

(b) 90% confidence interval for the mean price μ of all summer sleeping bags :

lower limit 67.92 $
upper limit 91.39 $