can u please solve the insolved questions with small explinations

The weight of anodized reciprocating pistons produced by Brown Company follows a uniform distribution with minimum weight 8.8857 pounds and maximum weight 10.3464 pounds. Suppose that 30 pistons are randomly selected a. The lightest 5% of the pistons produced, on an average, are rejected as underweight. What weight, in pounds, determines the underweight classification? Are pistons with average weight 10 pounds underweight? Solution: It is given that X -U(8.8857, 10.3464). The distribution of X- where u = 5(8.8857 +10.3464) = 9.61605 and o? = -8.8857 +10.3464)2 = 0.177804. Hence the 5" percentile is given by a = u-1.645 =9.61605-1.645(0.076986) = 9.407725. 30 So the piston with average weight 10 pounds is not underweight. b. The heaviest 5% of the pistons produced, on an average, are rejected as overweight. What weight, in pounds, determines the overweight classification? Are pistons with average weight 12 pounds underweight? c. Suppose that Brown Company cannot sell, on an average, lightest 2.5% of the pistons or the heaviest 2.5% of them. Can pistons with average weight 10.5 pounds be sold? Can pistons with average weight 10.2 pounds be sold? The weight of anodized reciprocating pistons produced by Brown Company follows a uniform distribution with minimum weight 8.8857 pounds and maximum weight 10.3464 pounds. Suppose that 30 pistons are randomly selected a. The lightest 5% of the pistons produced, on an average, are rejected as underweight. What weight, in pounds, determines the underweight classification? Are pistons with average weight 10 pounds underweight? Solution: It is given that X -U(8.8857, 10.3464). The distribution of X- where u = 5(8.8857 +10.3464) = 9.61605 and o? = -8.8857 +10.3464)2 = 0.177804. Hence the 5" percentile is given by a = u-1.645 =9.61605-1.645(0.076986) = 9.407725. 30 So the piston with average weight 10 pounds is not underweight. b. The heaviest 5% of the pistons produced, on an average, are rejected as overweight. What weight, in pounds, determines the overweight classification? Are pistons with average weight 12 pounds underweight? c. Suppose that Brown Company cannot sell, on an average, lightest 2.5% of the pistons or the heaviest 2.5% of them. Can pistons with average weight 10.5 pounds be sold? Can pistons with average weight 10.2 pounds be sold