Question

# A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest...

A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.

Find the probability that the mean actual weight for the 100 weights is greater than 24.9. (Round your answer to four decimal places.)

Weights have uniform distribution between a = 24 pounds and b = 26 pounds

Mean weight = (24+26)/2 = 25 pounds

Standard deviation =

=

= 0.57735

For sampling distribution with sample size, 100,

Mean = 25 pounds

Standard error =

=

= 0.0577

P( < A) = P(Z < (A - mean)/standard error)

P(mean actual weight for the 100 weights is greater than 24.9) = P( > 24.9)

= 1 - P( < 24.9)

= 1 - P(Z < (24.9 - 25)/0.0577)

= 1 - P(Z < -1.73)

= 1 - 0.0418

= 0.9582

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