The shape of the distribution of the time required to get ht

https//www.mathxl.com/Student/PlayerTest.aspx\'testld-105597461&ecenterwin-yes; Ramon Rodriguez 8/11/15 11:43 BOr Test Test Overvie The shape of the distribution of the time required to get an al change at a 20-minute ol -change facility is nkmou However, records ikate that the mean tme is zi·lmnes, and the staladea in himates Catplee pat (a)theough (c) (a)To composte prohallies seprée te sample mem mig te orinal mod! what tin tample would be required? OA The sample sice needs to be greater than er oqual to 30 OB Any sample sine could be used Oc The sample sixe needs to be less than or equal to 30 O0 The soemal medel cannet be used i the shape of the dssibution i surO b) wlhat i the robabliy hut a candsmn sample of n-3 al changes resuls in a sanmgle mesan tiew s than 20 tion The probabiley is approxtimately Round to foar decinal places as needed (c) Suppese the manager agrees to pay each emplovee a $50 boras if they mert a certains goat On a bpical Saturday. What mean (Ichange one would there be a 10% dance ofbeing al or below? This be the goal rstab ed by the 10 A M and 12 P JM Treating this as a rasdom samgle Ssbmit Test

Solution

a)

OPTION A: The sample size needs to be greater than or equal to 30.

b)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    20      
u = mean =    21.3      
n = sample size =    35      
s = standard deviation =    3.7      
          
Thus,          
          
z =    -2.078622626      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z >   -2.078622626   ) =    0.018826025 [ANSWER, PART B]

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Please resumbmit a clearer image of part C. Thanks!