A manufacturer knows that their items have a normally distributed length, with a mean of 6.8 inches, and standard deviation of 0.7 inches. If 4 items are chosen at random, what is the probability that their mean length is less than 7.2 inches? (Give answer to 4 decimal places.)
Solution :
Given that ,
mean = = 6.8
standard deviation = =0.7
n = 4
= 6.8
= / n = 0.7/ 4=0.35
P( < 7.2 ) = P[( - ) / < ( 7.2 -6.8) /0.35 ]
= P(z <1.14 )
Using z table
= 0.8729
probability=0.8729
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