1-The weight of gravel, in kilograms, collected by a power shovel may be modeled by a normal distribution with unknown mean, , and standard deviation

1-The weight of gravel, in kilograms, collected by a power shovel may be modeled by a normal distribution with unknown mean, µ, and standard deviation 50. The weights of a random sample of 20 collections have a mean of 1030 kg.

Answer the following questions round all FINAL answers to two decimal places.

(a) What is the point estimate of the mean weight of gravel that the shovel can collect?

(b) Calculate the margin of error for a 99% confidence interval estimate of µ

(c) State the 99% confidence interval for the mean, µ ( , )

d) What sample size is needed so that the error is no more than 15 kg. n =  power shovels

2- For an Economics test the mean score is 100 and the standard deviation is 10, and for an Accounting test the mean score is 50 and the standard deviation is 4. You are given the test scores of a student who took both tests. Determine on which test the student had a better score.

Enter E if the student did better on the Economics test

Enter A if the student did better on the Accounting test

Enter S if the student did relatively the same on both tests.

A student scores 130 on the Economics test and 61 on the Accounting test.

The student did better/same on test.