Math 211

Written Homework # 5

I have attempted this assignment honestly and the material submitted is my own work. I have only worked with the other group members listed on this page. I have not copied from any source, and cited any materials I have used outside of lecture notes and the textbook.

Names: Signatures:

Chapter Objectives (ch 16, 17, 18): Use Geometric and Binomial Distributions to compute probabilities.

Use sampling distribution models to make claims about the population Construct a Confidence Interval for a Population Proportion

Due Date: Monday, July 31

Statistics Summer 2017

1 The archer from the Chapter 16 Worksheet (Bernoulli Trials) buys a new bow in hopes of increasing her accuracy above 80%.

On her first day using it, she hits bull’s-eyes in the first 3 shots she takes. Do you think the new bow has increased her accuracy?

She also hits the bull’s-eye the next 3 shots she takes (6 in total). Now do you think the new bow has increased her accuracy?

Suppose 45 out of her first 50 shots are bull’s-eyes. Is this reason to believe that the new bow has increased her accuracy?

Give statistical reasons to support your claims.

2 On 85% of days I bike to school, it takes me less than 30 minutes. In a random sample of 100 days that I biked, what is the probability that my ride was less than 30 minutes on 90% of these days?

The distribution of the time it takes me to bike to school is skewed left with a mean of 24 minutes and standard deviation of 5 minutes.

(a) Explain why you cannot determine the probability that a ride is less than 20 minutes.

(b) Estimate the probability that the next 4 days will all take more than 30 minutes.

(c) Is it likely that the next 10 days has an average ride of less than 20 minutes?

3 We guess that 75% of Seattleites enjoy the outdoors.

(a) How many people must we survey in order to estimate the proportion of people who enjoy the outdoors to 8% with 90% confidence?

(b) Suppose we want to cut the margin of error to 5%. What is the necessary sample size?

(c) What sample size would allow us to increase our confidence level to 95% while reducing the margin of error to only 2%.

(d) For each of the above, construct the appropriate confidence interval and explain what it tells us.

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