1. Two students are arguing and one states, " Most the students at our school want a new mascot. " " No way We like being the Earthworms, " says the other. To settle the argument, they sample 40 random students to see what proportion want a new mascot. The friends are unaware that 38% of students want a new mascot. What is the probability that the sample supports the argument that " most" students want a new mascot?

2. A delivery company claims to deliver 90% of its packages on time. An online store, which has shipped thousands of packages with the delivery company, tracks a random sample of 100 recent shipments and finds that only 85 were delivered on time.

a)Assuming the delivery company's claim is correct, what is the probability of observing a sample proportion( with sample size n 100) within 5% of the true on-time delivery percentage?

b) Should the online store believe the delivery company's claim?

3. Marla has a vast library of over 8,000 songs loaded onto her computer. The mean song length is 210 seconds, and the standard is 48 seconds. Her computer has an option to send 50 random songs from her computer to a playlist on her phone.

a) Describe the sampling distribution of the sample mean song lengths for random samples of 50 songs sent to Marla's phone.

b) Marla goes on a three-hour road trip, what is the probability that she has time to listen to all 50 randomly selected songs during the drive?

4. Robert is trying out for his school's swim team. His favorite event is the 100-yard freestyle and,to make the team, he must swim the event in less than 58 seconds. Recently, he has been timing himself and believes his average time event is 57.4 seconds with a standard deviation of 0.8 seconds.

a) At tryouts, he gets to swim the event once while being timed by the coach. Can you determine the probability that Robert will make the team when he tries out?

b) Robert's friend Hailey took AP Statistics. She looks at his past times for the event and thinks their distribution is approximately Normal. Assume Hailey is correct and calculate the probability that Robert will make the team when he tries out.