Question

A production line is filling bottles of water where the volume of water in the bottles produced follows a normal density function with mean 1000 ml and standard deviation 0.4 ml. (a) What percentage of the bottles will have less than 1000.6 ml in them? (Round your answer to the nearest integer.) % (b) What is the probability that the amount of water in the bottle is not less than 999.5 ml? (Round your answer to one decimal place.) %

Answer 1

solution

(a)P(X<1000.6 ) = P[(X- ) / < (1000.6 -1000) /0.4 ]

= P(z <1.5 )

Using z table

= 0.9332

answer=93%

B)

P(x > 999.5 ) = 1 - P(x< 999.5 )

= 1 - P[(x -) / < ( 999.5 -1000) /0.4 ]

= 1 - P(z <-1.25 )

Using z table

= 1 - 0.1056

= 0.8944

probability=0.8944

answer in percent=89.4%

probability=