13. 312 points I Previous Answers llowskylntrostat16HW8 My Notes Ask Your Thuy D

Question

13. 312 points I Previous Answers llowskylntrostat16HW8 My Notes Ask Your Thuy Dau, Ngoc Bui, Sam Su, and Lan Voung conducted a survey as to how long customers at a clothing store claimed to wait in the checkout line until their turn. Let X time in line. Below are the 0.50 3.75 4.75 5.75 8.00 2.00 4.00 4.75 6.00 8.2S 2.25 4.004.75 6.00 8.25 2.25 4.25 4.756.25 8.25 2.50 4.25 5.00 6.50 8.25 2.50 4.25 5.25 6.75 8.50 75 4.50 5.25 6.75 8.75 3.00 4.50 5.50 7.00 9.75 3.00 4.S0 5.50 7,00 9.75 3.25 4.75 5.75 7.75 10.75 O Part (a) Calculate the sample mean x and the sample standard deviation s. (Round your answers to two decimal places.) x5.44 s=2.15 X min x min

Explanation / Answer

Solution:
Given data is 0.50,2.00,2.25,2.25,2.50,2.50,2.75,3.00,3.00,3.25,3.75,4.00,4.00,4.25,4.25,4.25,4.50,4.50,4.50,4.75,4.75,4.75,4.75,
4.75,5.00,5.25,5.25,5.50,5.50,5.75,5.75,6.00,6.00,6.25,6.50,6.75,6.75,7.00,7.00,7.75,8.00,8.25,8.25,8.25,8.25,8.50,8.75,9.75,9.75,10.75

Sum of terms = 0.50 + 2.00 + 2.25 + 2.25 + 2.50 + ?+ 10.75 = 272.25

Number of terms n = 50

Mean =Sum of terms/Number of terms

mean x-bar = 272.25/50 = 5.445

Part (a) : => Mean x-bar = 5.45 (rounded)

=> The standard deviation of the data set is s = 2.28 (rounded)

Part (d) :   
=> The distribution of X can then be approximated by X ~ NORMAL (? = 5.45 , ? = 2.28)

Part (e) :
=> P(x < 6.6) = P((x - ?)/(?/sqrt(n)) < (6.6 - 5.45)/(2.28/sqrt(50)))

= P(Z < 3.5665)

= 0.9998

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