The quality control team for an exercise equipment manufacturer randomly inspects 35 steel plates to ensure they each weigh ten pounds. The plates are used in various exercise machines. The average weight of the plates produced in the facility is 10.00 pounds, but the standard deviation of the weights is 0.25 pounds, which is not negligible. Find the probability that a random selection of 35 of these ten-pound plates has an average weight of between 9.90 and 9.95 pounds.
Round your Z value(s) to two decimal places. Do not round any other intermediate calculations. Enter your answer as a decimal rounded to four places.
Probability =
Solution :
Given that,
mean = = 10.00
standard deviation = = 0.25
_{} = / n = 0.25 / 35 = 0.0423
= P[(9.90 - 10.00) /0.0423 < ( - _{}) / _{} < (9.95 - 10.00) / 0.0423)]
= P(-2.36 < Z < -1.18)
= P(Z < -1.18) - P(Z < -2.36)
= 0.119 - 0.0091
= 0.1099
probability = 0.1099
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