Question

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.)

Answer 1

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