Question

The shape of the distribution of the time required to get an oil change at a 10-minute oil change facility is unknown. However, records indicate that the mean time is 11.1 minutes, and the standard deviation is 4.4 minutes. Complete parts (a) through (c). (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? A. The sample size needs to be less than or equal to 30. B. The sample size needs to be greater than or equal to 30. C. The normal model cannot be used if the shape of the distribution is unknown. D. Any sample size could be used. (b) What is the probability that a random sample of n= 35 oil changes results in a sample mean time less than 10 minutes? The probability is approximately (Round to four decimal places as needed.) (c) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 35 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, there would be a 10% chance of the mean oil change time being at or below what value? This will be the goal established by the manager. There is a 10% chance of being at or below a mean oil change time of minutes. (Round to one decimal place as needed.)

Answer 1

solution Given mean = 11.1 S.D(O)=4.4 a) The sample size need to be greatu than or equal to 30 N=35 PLXC10) - Pl X-4 olm < 10-1111 4.4135 PlzC -1.4790) = 1- Plzc1.4790) =1-0.9306 = 0.0694 © PIX<X) = 0.10 P18-M x-11) The 24/6)=0:10 X-11.1 41411631 = '1610) 2-11:1 =-1:28 4.4135 x=-1.28*4:Miss tll. x= 10.14801825 X-1011

a) liv - 700 64 = uxtox=740 OK= 740-700 660 700 ux-6x ux 740 uto = 40 normal © The Shape of the population is @ 22 - 40 19 - = 40 3 =13.3333