Question

12. A recycling plant compresses aluminum cans into bales. The weights of the resulting bales are known to have a mean of 100 pounds and a known standard deviation of 6 pounds. A simple random sample of 36 bales is taken. What is the probability that the bales will weigh, on average, less than 102 pounds?

a. 0.9772

b. 0.8334

c. 0.5293

d. 0.0002

13. Using the data in #12 above; what is the probability that the average weight of the bales is less than 98 pounds?

a. 0.8853

b. 0.3156

c. 0.0228

d. O.0114

Answer 1

Solution-12: Population mean 100 Population standard deviation = σ = 6 Sample size -n 36 Probability that the bales will weigh, on average, less than 102 pounds P( Z-score for( 102 < 102) 102 100 6/V36 z = 2.00 Hence, P < 102) = P(z < 2.00) From normal distribution table; P(z < 2.00) 0.9772 Hence, probability that the bales will weigh, on average, less than 102 pounds 0.9772 Solution-13: Probability that the average weight of the bales is less than 98 pounds P Z-score for (x98 < 98) 98 100 6/V36 Z2.00 Hence, P(X < 102) = P(z <-2.00) From normal distribution table: P(z < 2.00) 0.0228 Hence, probability that the average weight of the bales is less than 98 pounds 0.0228