A manufacturer knows that their items have a normally
distributed length, with a mean of 19.5 inches, and standard
deviation of 1.6 inches.
If 7 items are chosen at random, what is the probability that their
mean length is less than 19.9 inches?________________
Round your answer to four decimal places.
Solution :
Given that ,
mean = = 19.5
standard deviation = = 1.6
n = 7
_{} = 19.5
_{} = / n = 1.6 / 7=0.6047
P( <19.9 ) = P[( - _{} ) / _{} < (19.9 -19.5) / 0.6047]
= P(z <0.66 )
Using z table
= 0.7454
probability=0.7454
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