Name: Jorsely Galvez
Spring 2024
MATH220 Statistical Methods
Professor L. Collins
Show all work neatly and in order. You may use a calculator if necessary.
1. (18 points) A survey conducted over
days determined that, on average, 12.1 tons of space
debris collides with Earth each day. The standard deviation is 3.4 tons.
a) What is the z-score that corresponds to a 92% confidence?
b) Find the margin of error, E, for a 92% confidence.
c) State the 92% confidence interval for the average amount of space debris that
collides with Earth each day.
2. (18 points) In a random sample of 28 sports cars, the average annual fuel cost was $2929 and the
standard deviation was $786. Assume the annual fuel costs are normally distributed.
a)
Construct a 90% confidence interval for u. Interpret the results.
b) Construct a 99% confidence interval for u. Interpret the results.
c) Explain why your answer in part (a) should be a smaller interval than your answer
part (b).