A manufacturer claims that the life span of its tires is 500

A manufacturer claims that the life span of its tires is 50,000 miles. You work for a consumer protection agency and you aretesting this manufacturer\'s tires. Assume the life spans of thetires are normally distributed. You select 100 tires at random andtest them. THe mean life span is 49,848 miles. Assume ó =800 miles. Assuming the manufacturer\'s claim is correct, what isthe probability the mean of the sample is 49,848 miles or less

Solution

Mean ( u ) =50000
Standard Deviation ( sd )=800
Number ( n ) = 100
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
a)
P(X > 49848) = (49848-50000)/800/ Sqrt ( 100 )
= -152/80= -1.9
= P ( Z >-1.9) From Standard Normal Table
= 0.9713                  
P(X < = 49848) = (1 - P(X > 49848)
= 1 - 0.9713 = 0.0287