Question

Revenue in a cosmetics company comes mostly from their hair products' sales. The marketing department wants to estimate the proportion of customers who buy shampoo. How many customers do they need to sample to get a confidence interval for the true mean at 98% confidence level, with an error of +/- 0.02? 1. A heating and cooling company advertises that any customer buying an air conditioner during the first 16 days of July will receive a 25 percent discount if the average high temperature for this 16-day period is more than five degrees above the average temperature in July. If daily high temperatures in July are normally distributed with a mean of 84 degrees and a standard deviation of 8 degrees, what is the probability that the company will give its customers the 25 percent discount? 2. A heating and cooling company advertises that any customer buying an air conditioner during the first 16 days of July will receive a 25 percent discount if the average high temperature for this 16-day period is more than five degrees above normal. Daily high temperatures in July are normally distributed with a mean of 84 degrees and a standard deviation of 8 degrees. If we select 10 customers that purchased an air conditioner during the first 16 days of July, what is the probability that exactly eight of them (not more and not fewer) will have received the discount? 3. A heating and cooling company advertises that any customer buying an air conditioner during the first 16 days of July will receive a 25 percent discount if the average high temperature for this 16-day period is more than five degrees above normal. Daily high temperatures in July are normally distributed with a mean of 84 degrees anda standard deviation of 8 degrees. What is the probability that there aren't any days over 80 degrees in the first 16 days of July? A phone company offers unlimited data plan and a new free cell phone when you open a second line. If 50% of the customers qualify for that promotion, what is the error term at 90% confidence level, for a sample of 100 customers?

Answer 1

(Please round the answers to the required number of decimal places.)

(A) Q = 0.02 , 0.02 , Zam Z0.013 2-326 , b = 0.5, £= 0.02 in a sample size = (2x1).p(1-P), 3382.4] - 3382] (approx) (1) X~N/24,8). o ~ N(84,422) » &^w/84, 3). To find, P (* >89) = P(Z > 89-24 ) = P(Z > 2.5) =10.0062] (2) .n=10, Þ= P(>89) = 0.0062 Y~ Bin (10, 0.0862). To find, a ply28) = (s) por (14p)-10.0000). 01) * ~ N(84,2) To find, P(x280) = P(22-2)=10.0228] (B) E= Zx12. n = 100, P = 0. s a=0.10, ZX2= 20.05= 1,645 = 10.0822) Cs Scanned with CamScanner