Question

Chec Efficient manufacturing: Efficiency experts study the processes used to manufacture items in order to make them as efficient as possible. One of the steps used to manufacture a metal clamp involves the drilling of three holes. In a sample of 100 clamps, the mean time to complete this step was 54.5 seconds. Assume that the population standard deviation is a 8 seconds. Guided Show Part 1 Construct a 99.5% confidence interval for the mean time needed to complete this step. Round to one decimal place, if necessary. Ask My Link to A 99.5% confidence interval for the mean is 52.3 < < 56.7 Tal Fom Part 2 out of 2 Find the sample size needed so that a 98% confidence interval will have margin of error of 1.5. (Round the critical value to no less than three decimal places.) Save fo Sub Assige is needed in order to obtain a 98% confidence interval with a margin A sample size of error of 1.5.

Answer 1

S Answer : Given data lon=100 T = 54.5 seconds ! 6 = 8 seconds Cle 99,5 % / Part Il tramon . Construct a 99.5% confidence interval for the mean time needed to complete this Step. . 100(1-2) confidence interval for mean i pf x-Za o sek x + 2 5 ] = 1-9. 2 first find critical value. n evient Critical value is + za ble know that woning Clai-a d=1-c2 :x=1- 0.995 = 0.005 critical value () 20.0,05 = + 70.0025 i 20.0025 = + 2.80 critical value &2a - +2.80 : 99.5% confidence interval for the mean is Pf54.5 - 2.80 XO 54.5 +2.80 x Joyce 5- 2,24 Lalla 54.5+ PS 52.26 < < 56.74] =18

OR 52.3 celc 56.77=1-2 for the Ans: A gg.sy confidence interval mean is ( 52.3 <ll< 56.7) Part II Answer: Ginen data Cl=98%. E = ME= 1.5 find sample ... We know that size.co =2 first find critical value. zen - Zocos - Zoom Z z o. op 25= 2.3263 Clzlnd galacz e l-0.98 220.02 - - Erząc 5 = 2.3263 x 8 Un = 1. 2.3263 X 8 taking square on both side ne (2.3263)?x8? = 346.3424 (1.532 2.25 in na 153.9299 ~ 154 Ans: A sample of size of To=154] is needed obtain a 98% confidence interval with a margin of 1.5 order to onson