A machine designed to cut steel tubing into 2.4 metre lengths produces pipes with lengths that arenormally distributed with a mean 2.4 metres and standard deviation 0.03 metres.A random sample of 9 pipe lengths is measured. Which of the following is the most accurate description of the distribution of the sample mean length?Question 2Select one:a.It has a mean of 2.4 metres and a standard error of 0.01 metres.b.It is normal with a mean of 2.4 metres and a standard error of 0.03 metres.c.It is normal with a mean of 2.4 metres and a standard error of 0.01 metres.d.It has a mean of 2.4 metres and a standard error of 0.03 metres.

The distribution of lengths of salmon from a certain river is approximately normal with standard deviation 3.5 inches. If 10 percent of salmon are longer than 30 inches, which of the following is closest to the mean of the distribution? 26 inches 28 inches 30 inches 33 inches E 34 inches

Giant weta, native to New Zealand, are among the largest insects in the world. Their body lengths have a mean of 90 mm and a standard deviation of 3.6 mm.The lengths of a random sample of 36 giant weta is measured. Which of the following is the most accurate description of the distribution of the sample mean length?Select one:a.It is normal with a mean of 90mm and a standard error of 3.6mm.b.It has a mean of 90mm and a standard error of 0.6mm.c.It has a mean of 90mm and a standard error of 3.6mm.d.It is normal with a mean of 90mm and a standard error of 0.6mm.

The defect length of a corrosion defect in a pressurizedsteel pipe is normally distributed with mean value 30 mmand standard deviation 7.8 mm [suggested in the article“Reliability Evaluation of Corroding PipelinesConsidering Multiple Failure Modes and TimeDependent Internal Pressure” (J. of InfrastructureSystems, 2011: 216–224)].a. What is the probability that defect length is at most20 mm? Less than 20 mm?b. What is the 75th percentile of the defect length dis-tribution—that is, the value that separates the small-est 75% of all lengths from the largest 25%?c. What is the 15th percentile of the defect lengthdistribution?d. What values separate the middle 80% of the defectlength distribution from the smallest 10% and thelargest 10%?

Bolts produced by a machine have a mean weight of 50gm and a standard deviation of 2gm. If 300 random samples of size 36 are drawn from this population, determine the expected mean and standard deviation of the sampling distribution of means.a.mean = 50gm, sd = 0.33gmb.mean = 50gm, sd = 2gmc.mean = 8.33gm, sd = 0.33gmd.mean = 8.33gm, sd = 2gm

(g) Customers buying computer parts supplied by a certain manufacturer require that the parts be between 9.9cm and 10.5 cm, inclusive. The manufacturing process is such that the actual part lengths are well approximated by a normal distribution with mean 10.1 cm and standard deviation 0.20 cm. Determine the percentage of the manufacturer's production that is acceptable to the customer. (5 marks)